I'm putting a new bathroom fan in. So far I've put 3 fans in and none of them seem to pull the air from the room. I put a tissue near the fan and it doesn't grab it until it right up against the fan. The room should use a fan that recirculates the air at 150 CFM, and the room is 320 cu/ft. When I go into the attic to check it the exhaust is blowing just fine. There seems to be no damper problems. I have more air circulation than I need; what's up? There is a 1 inch gap between the door and the floor.

Exhaust fans do not circulate the air they evacuate or exhaust it outside. To do that there must be an equal amount of fresh makeup air entering the building. Open a nearby window and see if the fan pulls more, your home may be too tight

I don't know what you expect. You admit the fan is blowing into the attic. Pressure moves a lot more air than suction. With a 1" gap, you should have enough air flow. Close the bath door, turn on the fan and use tissue strips at the floor gap. I bet you see air flow.

PS 320 cubic feet is a small bath 5x8? That fan should be fine.