Is the Budget Allocator robust to variations in attribution?

I'm trying to understand better how the budget allocator works. I ran 2 different models with the same variables except for how i handled the "season" variable (Prophet vs a Manual Approach). Both yielded different R2 (i was expecting this) and different revenue attributions but overall the budget allocators remained almost the same.

Is Robyn’s optimizer robust to variations in attribution, only adjusting spend when differences in response curves exceed a certain threshold? I'm trying to understand why it would yield almost the exact same recommendation even though the revenue decomposition is completely different.

Thank you!