My spouse retired from the military in April which is when his home of record changed. How do I reflect that so we don't pay the new state taxes for this few months?

You indicate his (and yours?) move in the My Info section, and what sate he (and you?) "Moved"from.

IF he had terminal leave associated with it, i "think' you use the date at the end of the terminal leave...ore perhaps better, his date of separation on his DD214.

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Indicating that "move" in the my info are should trigger the Part-Year tax returns for both state's forms.  (though a few states do part-year strangely).

The states will usually calculate a tax, or taxable income based on FULL-Year income, then ratio if down based on what parts you indicate belonged to that state.  BUT when you start each state interview, it may show a high tax until you go thru the actual interview to "allocate" what belongs to them.

Don't bother staring either state section, until you have filled out every scrap of the Federal section.  IF you change anything at all in the Fed section later, you may have to go thru the state parts all over again to get $$ correctly allocated.