Part-time resident in NY and NJ, W2 withholdings suggest a later move date than my actual. What should I file with?

I originally lived in NY, but moved out to NJ around March. My employer is in NY. I was originally expecting the move to be temporary but it became permanent for the year of 2020.

 

Based on my payslips, I notified my employer of the change around October of that year. On my W-2, boxes 15-17 put around 25% of my earnings as NJ wages (with 0 tax on them) and 100% of my earnings as NY wages.

 

When filling out my return, Turbotax asks for how long I was a resident of New York and asks me to calculate how much of my earnings were earned while in New York (as a fraction of how long I lived there) and the same for New Jersey. If I take the March date as when I made the move, a much larger fraction of my earnings would be NJ wages than the W-2 indicates.

 

Should I be filling my state returns based on the date of my original move, or would that cause issues?