The tank filled up with water. When I checked the air pressure, water came out. So I drained down the water and then refilled the tank with 40 psi air.

Is it normal for this to occur or is the bladder most likely leaking.
Will I end up having to change the tank.

Never changed the tank before, not sure I know how.

When I checked the air pressure, water came out. Is it normal for this to occur or is the bladder most likely leaking. Will I end up having to change the tank.
The membrane in the tank's ruptured. (see image) and you must replace the tank. I've put up how a bladder tank operates,(see image) so you will have some idea of its function.
Changing the tamk will be a simple operation. Simply purchase the same bladder tank and replace fitting by fitting. Don't frorget to Teglon Tape the threads, Good luck, Tom

Tom is correct, you will need a new tank.