A cut-in window has no effect on the optimal spine of the arrow. You can verify this with a bare-shaft test if you don’t believe it. However, the cut-in window does make arrows less sensitive to spine variation. With a cut-in window, tuning and shooting become easier because the arrows are less affected by spine variation, release inconsistencies, or other tuning issues. The wider the handle, the more sensitive everything becomes.
My point is that if the optimal static spine is, for example, 42#, it remains the same regardless of the handle width. But with a wide-handle bow, a 44# bare-shaft arrow may fly to the left (for a right-handed shooter), while with a cut-in window the same arrow may still fly straight.
Regarding the “correct” spine, it’s more of a statistical issue. I can shoot accurately with normal, fletched arrows even when the spine variation within the set is 10–15#. But arrows that don’t have the optimal spine will occasionally fly farther left or right. Over the long term, statistically, the arrows with the correct spine will land in the center most consistently. Again, it comes down to sensitivity to various factors (spine, bow, archer, etc.).