Another expert here, just wanting to be sure you understand it may not totally be good news.
It is not when the work was performed that will determine what is to be reported as a resident of New Mexico; but when it is paid. The only exception is if you use an accrual basis for accounting.
New Mexico residents have to pay state tax on all earnings, no matter where earned, during the time of being a resident.
You do not have earnings for tax purposes until you are paid.
So, whatever you are paid after you move to New Mexico is subject to state income tax.
You asked "Will I be liable for state income tax on money received for jobs done before the move even if paid later, or only for money received for jobs finished after the move?"
The answer is that you are liable for state tax on all that is paid after you move (even if the work was done before the move) since it is counted for tax purposes when it is paid. All that you are paid after you are a resident is what will have to be reported to the state.
Please ask if need more discussion or clarification.