Water comes out of shower and tub before I pull up shower plunger?

What is water pressure? Did installations instructions specify up and down. Perhaps obstruction in spout (tub) port or piping. Single lever or two handle valve? If single lever remove cartridge and flush valve. Get 1/2 pipe cap, remove shower head, install pipe cap. If you have obstruction in tub port you should be able to flush tub port with shower arm capped.

Harold touched on a very good point: Make sure the rough-in body is installed UP in UP position and Down pointing Down...

Back to you. Milo