This documenthttps://www.nj.gov/treasury/taxation/pdf/pubs/tgi-ee/git6.pdf seems to say, in several places, that you are taxed on income received while you were a NJ resident, e.g.
"part-year resident and may need to file a resident tax return to report the income received for the period you
resided here" (page 2).
This is the way it usually works, in most states, as HelenC12 said at the other TT (referenced) thread ("Generally, individuals are cash basis taxpayers. A cash basis taxpayer is a taxpayer who reports income and deductions in the year that they are actually paid or received.").
But, you may want to call the NJ tax people and get specific answer. Let us know what you find out.
Being double taxed is also not unusual. The first state may tax you because the bonus was earned there, the year before, and the 2nd state taxes you because it was received while you were a resident there. The 2nd state gives you a credit for tax laid to the 1st state. Since your 1st state (TX) doesn't have an income tax, you get no credit, in your case.
