Unless the leash and harness is on.

They don't rush the door.

Othello has been taught when the door opens go to my bedroom bathroom and he goes right back there until I tell him it's ok,come on out.

My cat Rustle would come to the threshold of the door but never step beyond the threshold. If I told him go to my room he'd go

And my three other cats I had at the time would go to my bedroom with him until I told them it was ok to come out.

Never had problems with any of my cats bolting out the door.