No water would flow out of the top of the filter with the pump off. The plumbing system doesn't retain pressure in it, it equalizes to atmospheric pressure when the pump stops. Think about it, both ends of your plumbing, inlet and outlet, are open to the pool. There's nothing trapping or creating pressure in the plumbing when the pump is off.
But water shouldn't leave the system either, the filter and pump and the pipes should stay full of water. If you open the air valve on the filter with the pump off, that "breaks the seal" and will let air into your filter and possibly the rest of the pool plumbing as well if you leave it open long enough. Then when you restart the pump, some of the air you just let in will get trapped in the filter, which you have to bleed off again by opening the valve again. By fooling with it, you might be creating the problem, which isn't really a problem so much as expected behavior.
Start the pump. Let the pump finish priming. Open the valve to bleed off any trapped air. Close the valve. Done. Leave it alone.
If you come back days later, after the pump has cycled on and off a few times from normal scheduling, you can check how it's doing. While the pump is running, open the valve. You should get no air, just water. That's how it should work. That's how mine works, anyway.
With no trapped air, and pump running at 1500RPM, I get about 5psi. I can expect that to rise a bit throughout the season. That's the indicator that my filter is capturing crud. That's all normal. The more the filter membranes get blocked by crud, the harder it is for the water to get through, so that increases the pressure in the system. I use the pressure gauge to monitor the filter's condition. When it increases a few pounds, I know it's time to clean the filter again.
When I open up my pump to clean out its leaf basket, that also lets air into the plumbing. I clean the basket, put it back into the pump, close it all up, then start the pump to watch it prime and fill with water. But now I've got some trapped air. So I open the filter valve and bleed it off until I get water spraying out, then I close the filter valve. Done. I don't fool with the valve again until I clean the pump basket again.