Fly,
Here is how it should work..
In your pic, the automated Return valve is set to Spa Off and Pool on..
The water goes to the left in your pic and most of it goes down and back to your pool returns.. BUT... Some of the water goes through the "make up" valve (the manual valve right below the Return valve).. then through the check valve and then to the spa.. It may go to the jets or another pipe, but this water is what adds water to the spa and makes it spillover into the pool.
If the spillover is not working then make up valve may be broken or the check valve may be stuck closed.
I suggest that you take the manual valve and the check valve apart and inspect them.. You should be able to turn the make up valve and adjust the amount of spillover. The check valve prevent the spa from draining back down into the pool when the pump is off.
Thanks,
Jim R.