As stated in another answer, there are basically two different kinds of indoctrination used by the Reapers. There is a slow and subtle version and more rapid version. It seems that for high-value agents the slow version is used, which actually subtly influences the target over months or even years instead of simply enslaving their will. This basically leaves them free to act on their own while they are actually influenced to serve the Reapers purpose.
Saren Arterius and Jack Harper (aka Illusive Man) both were such agents. In both cases there is evidence that they were slowly indoctrinated over the course of a few years.
In case of the Illusive Man the indoctrination might have begun when he first came into contact with Reaper tech on Shanxi during the First Contact War (this story is told in the comic book Mass Effect: Evolution). This happened several years before the games.
I believe it's nowhere clearly stated when the Reapers began to influence him, so the following contains speculations. But I think this is a very plausible scenario, given what we know about the Reapers' methods.
Jack Harper fought as part of the resistance against the Turians.
He and his friends managed to capture a Turian who turned out to be General Desolas Arterius (Saren's older brother). He was looking for an artefact on Shanxi. This artefact turned anyone who came close into a Reaper-augmented warriors who protects the artefact at all cost.
Desolas wanted to use this to create super soldiers called Meta-Turians. While fighting near the artefact, Jack's friend Ben comes into contact with it and is killed - only to return turned just like the Turians. Jack on the other hand, was only knocked unconscious and captured by the Turians.
The artefact left its mark on him, however. This is how he got is blue-glowing eyes. He could also feel the artefact and he started to have dreams about the impending doom of mankind. He knew that something terrible was coming.
It's unclear why he was only touched but not turned by the artefact. Maybe the contact was to short to turn him but enough to plant a seed.
His visions might have been part of his indoctrination. It were those visions, after all, that lead him to create Cerberus and to pursue technology in the believe that all technology can be mastered and used - even Reaper tech (although all attempts to do so backfired).
Some time after the events of Mass Effect 2 and after experimenting on Paul Grayson he began to use Reaper tech and thus sealed his own fate, turning quickly into a full Reaper slave.
But the horrible thing about the slow indoctrination is, that the agents are just influenced but not directly controlled by the Reapers. They start doing the wrong things for all the right reasons and until the end they believe that they are doing it for a good purpose. When they finally realize that they played into the Reapers hands, it's far to late for them to break away from their control.
The Illusive Man did really fight the Reapers and what he did was meant to make Cerberus (and mankind) ready to oppose them (including the revival of Shepard). But at the end he played into their hands when he became obsessed with the idea that he could control the Reapers and this lead to him opposing Shepard when he should have helped him instead.
And it's possible that the
Reapers put the idea in his head years ago.
Saren was the same. He kept believing that helping the Reapers was the only way to save his race and others from total annihilation. He also kept believing that he did it all of his own free will and that he was not under Reaper influence.