"Generally" the refund and any penalties and interest are calculated separately, that is, they tend to send you the refund and bill you separately for the penalties and interest.
But this can vary.
Have you received a letter from the state of New York for penalties and interest for 2017 and 2018 (I assume you have). Then that office (and agent, if one is named) has control of your audit experience (this is a "letter audit", not a big in-person audit).
You say that you have sent in your 2017 and 2018 returns, right? Then the thing to do is to respond to the author (office or agent) of the letter asking for the penalty and interest, tell them that you have filed both returns, apologize for the confusion, and ask for an abatement of any penalty and interest on those returns.
They probably won't abate (wipe out) the penalty, but you want them to realize that you didn't owe any interest after all, so that they mark your account as owing no interest and therefore won't send you any more letters once you have paid the penalty.
You want them to put this matter to rest so you can get on with things and not have to worry about tomorrow's mail.
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