In Time/WMG

The clock ticks are payment of a capitation tax.
No economy could function if its currency were vanishing rapidly the way time currency must if it just disappears. Everyone must come up with 1 year per year to survive, but the only time added to the economy is 1 year given to everybody on their 25th birthday. The most reasonable conclusion is that each second that ticks off each person's body clock goes to the government, who then uses it to pay for things like the Time Police or other services.
 * Problem with that: It assumes that the money can be transferred remotely by the government, in which case they could have just taken all of Will's time no matter where he was. My guess is that new time is added as needed to the economy (mostly being given to the rich), but at a rate to keep the underclass down.
 * This is exactly how it's done IN REAL LIFE. Central banks print money and loan it to regular banks (like Weiss), which loan it to people. Each injection causes inflation, which makes prices rise more and more. In theory, anyone could become rich through hard work and frugal living. In practice, new money makes saved money WORTH LESS. Welcome to Crapsack World.
 * It is, undoubtedly, a controlled economy with a capitalistic veneer.
 * Unless the level of economic transformation isn't uniform, which it undoubtedly isn't, despite each country pledging to it . The nations with zones could easily represent a unified economic bloc, and they still need things that aren't necessarily manufactured in their own zones (from cars to concrete). Each collection of zones being its own industrial fiefdom is a lot less likely, so the less developed time economies or anyone else makes up the difference through trade. The local economies are the domain of either the government, or corporations like Weis, who control the amount of currency in large part, or entirely--either group might not care how many people die in the lowest ghetto as the economy periodically shuffles people down zones. Though whether formal government (with no uniformed police or symbols of authority) or a cabal of Weis-like corporations runs things probably doesn't matter to the man at the bottom, one is still a capitalist economy.

The clock is what kills each person.
The concept of the clock and it's use of time as currency is all in place to prevent overpopulation, with the clock itself being the cause of death. People stop aging but are implanted with this device to insure they die at some point in the future when ' You Have Outlived Your Usefulness '. Either the device emits a strong poison or electrocutes to cause death, so by earning more time you are only prolonging your own death sentence.
 * The device would have to be applied in such a way that removing it would result in instant death otherwise everyone would just remove them. ("Hey, what's an arm if it means I can live forever and maybe make a new one?")
 * As the below Wild Mass Guess states, perhaps the mechanism is not one that triggers death, but which prevents it, and adding time to it constantly replenishes it. So the clock is not what kill each person - it's what keeps each person alive (possibly).

Both rich and poor are victims of science.
The 25-year span plus whatever looks involuntary at this point. It may be that the people in this society are inheritors of earlier experiments regarding cell-division and aging. The goal was less true immortality than one's body remaining "forever young", hence the 25-year cutoff point. People rushed to embrace the apparent miracle, believing they could avoid the illnesses and debilitation of aging, only to realize they'd also sacrificed the next fifty years of natural life for one enhanced one. By now their bodies can't switch off the immortality gene, so to stay alive it has to be replenished, hence time is as vital to life as food, water, oxygen. The wealthy learned to do this first, accumulating their years in the process, keeping the system in place in order to thrive.
 * Most likely the system was voluntary when it started. When a way was discovered to stop aging, the government imposed some kind of time limit on how long you could live, and the clock was born. Original lifespans might have been much longer, so most people would flock to live 100 years without ever growing old. But at some point, people were allowed to buy, sell and trade time, and eventually it displaced all other currencies. Naturally, this meant that the wealthy would live longer. and the wealthiest people started scheming to control the economy and reduce lifespans for everyone but themselves. Lifespans were reduced slowly enough that, by the time free time was down to 1 year, everyone was already locked in.

Aliens did it & The true evil
Considering the current technology level. I'm thinking that at some point in an alternate history, aliens came down (for whatever reason) and infected everyone with this condition. Society adapted around this and even found a way to artificially transfer time between devices. Maybe it just works like bitcoin, and people found a way to "mine" for more time? It is also possible that there is a class lower than those seen in the movie. This class is simply slaves which are bread and raised in cages, producing children as young as possible. When they hit 25, all their time is siphoned off and they are killed.

Timekeeper Leon's "way out of the ghetto"
...was being a Minute Man like Fortis. He's familiar with the "mass murder" being carried out in the ghettos, but waves it off. Also, people drop dead in the street every day, and are ignored - so how did he know Salas' father? Answer: Salas's father wasn't a Minute Man, but a vigilante - he stole back time from Minute Men, until he ran afoul of Leon. Who beat him, stole all his time, then took the ultimate reward for Minute Men - promotion to Timekeeper.
 * This Crapsack World just got even crappier.
 * While Leon starting out as a Minute Man makes absolutely a lot of sense, he repeatedly claims to have fifty years of experience as a Timekeeper. The timeline doesn't work out for him to have met Will's father that way.

The people of this 'verse are humanoid Cylons
The creators of this particular batch built the rechargeable timeout into the system in order to keep them in line. However, they left a fatal flaw in the system that allowed one Cylon to steal time from another. The ones who became the aristocrats of this world are the ones who figured out how to profit from it, giving them the resources to destroy (or possibly outlive) their creators and become the new masters.

South Park was the inspiration to this movie
I just watched "The Biggest Douche in the Universe" for the first time in a while, and the doctor keeps talking about how Eric is fine, except he is running out of time. He needs a time transplant.

The people who originally set up this system are long dead.
Being from simpler times, they were reckless in addition to being immortal - went swimming in the ocean, bungee jumping, off roading, and eventually statistics caught up with them.

There are HUGE orphanages out of view.
You have a kid - how are you going to be sure you'll be around to see it turn one month old, let alone one year!

Mothers to be are granted one year for the pregnancy.
...and this isn't helping the population problem.

There is a One Child policy or something similar in this world.
We don't see that many children around and there's no mention of anyone having a brother or sister.

Leon and Fortis have history.
They're the same age, Leon's a cop who grew up in Dayton and Fortis is the leader of the ... only gang in Dayton, apparently. Depending on when exactly Fortis came to Dayton from Britain, it's hard for me to believe their paths never crossed. Share Start of Darkness? The reason Leon became a Timekeeper? A doomed friendship? Fanfic writers, get on it.

The Time/Money system evolved from universal health care.
"Turning off the aging gene" is shorthand for a set of drug implants and metabolic overrides that not only prevent aging, but prevent disease and heal the subject of anything less than an instantly-fatal injury. Will and Sylvia crash a sports car and are running just minutes afterwards(though that means Borel chugged several dozen gallons of high-proof booze to overtax his implants).