Indeed, that's former stray behavior. He's trying to go back to his territory. You have to be very careful that he doesn't go out for at least a month so he starts identifying your home as his territory.
I have 3 former strays, 2 still go out (one of them will drive me crazy if I don't take him out every day) and the third is too afraid to go anywhere, so she doesn't go out at all.