Yes, there are two things working in concert. At any time, throwing the lever, releases the cable and the FD's spring moves it inward. But the variable here is the chain tension. When it's low the FD cage gently pushes the chain over, but when it's higher, it initially resists disengaging from the larger ring, and when it finally does it snaps the chain inward much faster. In fact if the tension is high enough, it can hold the chain so tightly to the larger ring that it won't shift at all.

So as I said, the character of the shift is different under load. You have a bike that shifts well under normal conditions and overshifts when under load. So, like the doctor joke, the solution is to not shift that way. It takes very little thought to anticipate FD shifts, and change the sequence and avoid FD shifts under load.