For ISOs, you're only subject to AMT on the spread between fmv and strike price at exercise. However, since there is (I think by law?) a 90-day exercise window after leaving employment, there's only 2 circumstances: (1) exercise while employed, and (2) exercise w/in 90 days after leaving employment. In both cases you're almost certain to be a resident of the state in which you were employed. Nothing I know of would require you to pay AMT to the state in which you were granted the options you exercised, but because it's unlikely for you to be a resident of a different state, it's a less interesting question.

Also, if your company takes off like a rocket, it's very much in your interest to not procrastinate on exercising vested options, because you want to minimize the AMT-taxed spread between FMV and strike. That increases the likelihood you're a resident of the state in which you were employed when you exercise.