I've concluded that usually they do not put you into a first-come queue when you check in. They still seat you at your reservation time, more or less. I think what happens is that you are the "first" person at the 7:15 slot, since you checked in at 6:45. All the other 7:15 people will be after you (unless a table needed for your size party isn't ready first).
In the meantime, all the 6:50 and 7:00 people will be seated before you, even if they arrive four minutes after you did and check in.
I can't be sure this is true at EVERY restaurant, but I've seen in multiple times recently.