Truck pulls forward when parked

Just curious what you all think. I have been driving manual most of my life.

This is a second auto transmission I ever own. When I enter a parking space, I would brake, then put it in "P". Finally, press the foot brake and turn off the engine. I notice the truck pull forwards more than any other auto I had driven.

My worker told me to put in neutral first. Just an observation of the new truck

 

Any automatic trans will roll slightly until the parking paw catches. Doesn't sound like there is anything wrong.

 

I think so too.

 

Are you on the level?.... I mean parking "on the level".....If facing down a steep grade, I can maybe see some movement: however, If you put it in PARK...set Park brake...and THEN shut it down (when on the level)...and it surges forward....???? Sounds like an issue to me....

Over