Oh, apparently for NSOs. That is not true for ISOs, which the vast majority of startup employees will be granted. see Publication 1004 from the CA Franchise Tax Board, discussing ISOs [1]

   Nonresident of California on Date of Stock Sale
   Qualifying Disposition
   If you exercise an incentive stock option while a California resident or a 
   nonresident and later sell the stock in a qualifying disposition while a 
   nonresident, the income is characterized as income from the sale or 
   disposition of intangible personal property having a source in your state of 
   residence at the time you sold the stock. Accordingly, you are not subject 
   to income tax by California even though the services that gave rise to the 
   grant may have been performed in this state. [pg 10]

[1] www.ftb.ca.gov/forms/misc/1004.pdf

This covers the stock sale, but what about the liability of taxes from the exercise (diff between strike price and current value)?

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.