Warning: This page contains major BioShock spoilers. Proceed at your own game-ruining risk!
You were born in Rapture
So how and when did Fontaine mess with your mind? At the very beginning.
No, not the beginning of the game... you were under his control well before then. He got to you when you were nothing more than a baby. He raised you to be his slave. He and a mad doctor experimented on you, transforming you into a genetic superman. They forced you to prove your loyalty through murder. They taught you to obey.
And then they sent you away from Rapture, ready to be called back when they needed your blind subservience the most. The plane crash wasn't an accident - you were told to hijack it. The memories in your head? The sudden flashes of a home and of a family? Fabricated and planted by Fontaine. Sorry.