Somebody, after the fake saint was exposed while the kingdom went to hell in a hand basket, figured out what had happened.
It isn't the father. It would have been far more effective to keep his own memories and insure that he didn't fall for the ruse, thus also shielding his real daughter from the awful memories.
It could have been the brother or the prince or the knight. Maybe even the princess, a recently introduced turns-out-she's-a-good-person character.
The hole in this story is, how would any of these people know that Keira is aware that she herself was the real saint? She only knows it because of the meeting in the jail cell, just prior to her execution.
Perhaps somebody witnessed that meeting, but was unable to stop the execution in time, or the fake saint confessed, and told the authorities everything?
But all of these candidates would have been better served to keep the information for themselves, so they could know the truth while they could still prevent the tragedy.
Quite frankly, if it turns out to be the father, the prince, the brother, the princess, the knight... then the writer screwed up. All of these people are better served keeping the memory themselves.
Literally the only person that makes any sense whatsoever was the time magician himself. He found out everything after all these useful people and everyone else useful was dead (perhaps the fake saint bragged about what she did as the kingdom burned). He couldn't keep the memory for himself, so he unwound time for Keira and hope that, with the foreknowledge of her future, she would escape, or hide, or somehow survive until the fake saintess was exposed so she could appear and retrieve the situation.
It was still a bad plan. All he needed was someone he could trust to give him the information so he could save the situation himself. But perhaps all of his acquaintances from the time were already dead, and there was just no other choice.
So, what about the father's dreams? Perhaps it's a side-effect. The time magician just didn't mention that some people will have such dreams. Perhaps it's a fringe effect that acts upon people tied by blood to the regressor, in which case, it's actual proof that she's his daughter.