As @AnnetteB6 stated, there should not be an overlap for taxation since you moved and are filing part-year returns. The RSU transfer/granting/vesting income is included in your W2 box 1. When you allocate wages to CA and NY you will use the percentage of time you were in each state to divide the box 1 wages. If you also sold some/all of the RSUs whatever 1099-B income generated there, separate from your W2 wages, is taxed by the state you were in when the sale happened. There will be no credit for taxes paid to another state in your situation.
Even though the statements might show taxation of some income by both states, when you file your returns that is reconciled based on the correct allocation you make and if a state over taxed on the income that actually belongs to them you will be refunded by the taxing state; not credited by the other state.
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