Minor collision with my Yaris

[justjesus]

in california, that's fairly typical rates for a bumper replacement (through insurance)

as far as "who's at fault?" goes, that's a question of liability.

The main thing you got going for you is that you were in the "main thoroughfare" part of the parking lot. He was coming from the side. This gives you the right-of-way.
One detail I didn't see, and it's maybe because Im tired and it's late, is the point of impact to the other car. Which part of his car did you hit? Any claims adjuster/examiner worth a damn will want to know this.

If the damage was closer to the front of his/her car, it is more favorable to you. If it's more toward the back, it is more favorable to the other driver. Why?
Because if he pulled out enough to where you hit him/her toward the rear, then s/he was establishing "control" of the intersection.

It's not as easy as this, however, but that's almost what it boils down to.