The question, "For the years you received these distributions, was the total amount shown on the form the amount you paid tax on?" is referring to the total amount in Box 1 of Form 1099-R as compared to the amount in Box 2a. So, is the amount in Box 1 the same as Box 2a? If it is not, the answer would be "No".
Box 1 is not always the amount you pay tax on; it is the total gross distribution. You are usually taxed on the amount in Box 2a, which may be lower if you made after-tax contributions. If you rolled over the funds, the taxable amount could be zero.
You are correct; New York State excludes up to $20,000 of retirement income (per person) if you are 59 1/2 or over. The information from your Federal return will flow to your New York State tax return. The amount that you had withheld for New York State tax will be applied to your overall tax due or it will be refunded to you.
The fact that you had New York State tax withheld from your distribution won't affect how your distribution is treated on your New York State Tax Return.
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