State tax filing

Michael -  I have a question that you may be able to help with (I asked elsewhere too given I wasn't sure where to post) - here it is:

 

I am moving from FL to NC in mid October and have dividends that will arrive around that time.  Since FL is a tax-free state, I'd obviously not pay taxes when I'm here.  My question is - if I move to NC in mid-October and receive dividends that month (but the ex-dividend date was in September while I was a FL resident), are they re-portable on for NC given they were "earned" in September but paid in October?  This reminds me of my year-end 1099-B which states taxed in another year for some dividends even though I received it in a different year.  I hope that was clear - thank you.