No, the NM $600 stimulus was not sent automatically. Google search turns up the instructions, it will issue when you file your 2020 tax return, if you already qualify for the Working Families credit.
If you filed early and don't see that $600 refunded soon, maybe end of May, file an amended return. For ordinary tax refunds, the state of NM is lightning fast. So early filers should not have to wait long for the state to amend their return to credit the $600.
