You have 2 valve actuators. One is on the suction line, the other is on the return line. I believe that is correct from what I am seeing.
From a Pentair perspective, not Hayward, here is what happens for the modes:
Pool - SUCTION valve actuator set to pull from pool main drain/skimmers, RETURN valve actuator set to return water through pool returns.
Spa - SUCTION valve actuator set to pull from spa main drain, RETURN valve actuator set to return water through spa jets
Spillover - SUCTION valve actuator set to pull from pool main drain/skimmers, RETURN valve actuator set to return water through spa jets.
The Spillover mode utilizes the action from both valves to create the spillover.
Now if you have the RETURN valve actuator set to where it stops with the SPA side partially open, then it will always allow flow through the spa, regardless of what mode you are in. I have mine set like this to just allow a small trickle of water flowing over my spa at all times.
I believe that Hayward and Jandy likely use similar programming for this. I don't know how else you would do it, or why you would try to complicate it.
It sounds as if the plumber set the stops to allow the RETURN valve actuator to never fully close the SPA side of the valve, allowing constant flow through the spa returns. This is why he is saying you have to have the spillover at all times.
Plumber added the actuator, programmed the control and says I will no longer be able to have the spillover AND pool features going at once.
He is correct here in that if you have the return actuator set to fully close both pool side and spa side, you will not be able to have the spillover and water features at the same time, since all water will be directed to either the spa or pool. From what it sounds like, right now you do have spillover and pool features going at once and you don't want that.
To fix this I think all you need to do is reset the return valve cams to allow the spa returns to close fully, when in pool mode, and enable the spillover mode in the automation.
--Jeff