The water level in the tank and the sump should reach an equilibrium on their own, although it can take even as long as 5 or 10 minutes from when the pump first starts. This equilibrium is dependent on the pump speed, the overflow height, the size and type of the drain and a number of other factors.
But that said, taking water from the tank manually and putting it in the sump will not affect the water level in the sump for more than a few minutes. The lower water level in the tank will mean that not as much water will go over the overflow for a short time and the pump will pump more water back up to the tank than is coming down and the equilibrium will be reached once again.
If the drain size is too small or the pump is too big then the pump will pump more water up to the tank than the drains are able to handle. In that case the water level in the sump will keep lowering while the water level in the tank keeps raising until the sump runs out of water or the tank overflows, but it sounds like that is not what’s happening here. From what you’ve said it sounds like the system does reach an equilibrium at some point.
My guess is that you’re simply not waiting long enough for the equilibrium to be reached. As I said above, manually moving water from the tank to the sump will do nothing to change the water levels... they will go back to their original equilibrium after a short time, so there’s no need for you to do that. It is possible that it’s taking a little while for the drain to start siphoning and before that happens the pump might be out pumping the drain and that will lower the water level in the sump for a short time. But once the drain starts flowing at full speed it should come back up again on it’s own.
You don’t say how long you’re waiting after restarting the pump, but like I said above it can take 5 or 10 minutes or more for it to reach this equilibrium. I would suggest just watching it and waiting longer. Restart the pump and keep an eye on it just to make sure that the tank doesn’t overflow or the sump doesn’t run dry, but I suspect that if you give it long enough it will return to equilibrium on it’s own after a few minutes.