How you'll file and whether all of your income is taxable in New York depends on whether you're working remotely for your convenience or if your job necessitates your working out of New York. In both cases, you'll file a nonresident California return.
If your job requires you to work outside of New York, your wages wouldn't be subject to take in New York. The vested stock is taxable to New York based on how many days you worked in New York during the vesting period. The vesting period is the time between when the stock was granted and when it vests. If you were out of New York by the time the stock was granted, none of your vested stock income would be taxable to New York. If your stock was granted before you moved out of New York, some of your vested stock income would be taxable to New York.
If your job doesn't require you to work outside of New York, but you choose to - all of your income would be taxable to New York. This is called the convenience of the employer rule - remote workers that work for New York employers are treated as working inside New York. In this case, you'd file a nonresident return but allocate 100% of your income to New York. The income would also be taxable to California since you live there. California would give you a credit for the taxes you paid to New York to avoid double taxation.
When completing your New York return, you'll come across a screen that says New York Income Allocation and asks if all of your income was earned in New York State. Click No on this screen and then follow the prompts to allocate your income appropriately.
It's also important to note that New York starts with calculating income tax on your total income and then applies an income percentage to prorate the tax based on how much income you earned within the state. Therefore, sometimes it may seem like you're being charged tax on your entire income - but if you see an income tax percentage that's less than 100%, you're not really paying tax on the full amount.
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