While parts of the answer by @Valorum are credible, my interpretation is simpler.
The starting point is that Mal and Cobb had both been exploring deeper and deeper dream states. They had been building their own world in the dream state and it was something they were happy with. They spent a long time there. Mal was so happy she hid her token (the token is put in the safe) so she was no longer reminded that this was a dream state (the spinning top appears to be Mal's token, not Cobb's, at least originally. Though there is another theory that Cobb's real token is his wedding ring).
The key point appears to be that Cobb recognises that they both need to return to the real world, however happy they are in the dream world, but can't persuade Mal to return. This is why he tries inception: to (re)instill the idea that the world they are in is not real. This works and they do return to the real world.
But the problem with inception is that it sticks. Even in the real world Mal still believes in the idea. Hence her suicide.
In short, Cobb did not do anything to Mal's token to encourage her to believe the dream world was real. More like the opposite. She chose to believe the world was real because she was happy in it and hid her own token to conceal the evidence otherwise. Mal was not distraught about living in the dream world, the problem was she was too happy in it to want to leave. Cobb's action was to recover the token and to initiate the first inception on her to persuade her the world was not real (it is never stated or shown but the implication is that recovery of the token didn't persuade her).
As for the tokens and who owns them. Nolan–as is his habit in other movies–leaves a great deal of ambiguity so viewers can inject their own ideas. The spinning top is initially presented as Cobb's token. But, in some of the flashbacks to the backstory, it seems to be Mal's. But, after this, Cobb seems to use it as his. Hence the various theories about his real token. But whichever theory is correct, there is a clear implication in the dream world backstory that Mal hid her token because she was happy in that world and didn't want to be reminded the world was not real. This is what motivated Cobb to try inception, precipitating the remaining events driving the movie. But there is plenty of room for interpretation here leaving a far more interesting burden on the viewer and a wonderfully ambiguous ending that makes for a far better movie than a clear explanation would have done.