Yep, the houses moving the mailman is 100% intended. I don't think it breaks that first rule since you aren't in direct control of the mailman, and the only way of moving them around is via pushing them with the houses.
I also intended to imply that there are aliens outside of the screen borders, which is why if the mailman can no longer be seen by the player, they get abducted. This is more apparent when the dogs drag you offscreen.
I don't know how much more I'll work on this idea, but thank you for your feedback!