Even though the tax debt was allocated to you in the divorce, that divorce decree does not bind third parties such as the State. Since the State came after your ex for the tax debt, it appears that the two of you were jointly and severally liable. Under those circumstances, you ex [by virtue of the divorce decree] appears to have a right of indemnity to collect what he paid out from you.
As far as changing the support, it appears that he is not so much asking to change the support amount; but rather an offset for his losses on the tax issue.
I know this is not the answer you wanted to hear, but I am assuming that you are paying for a professional and honest answer.
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