"For me it is confusing"

I describe it like this:

If they got the benefit of their State tax payment(s) as a "write off" (deduction) and then later get some of it back as refund, they need to claim the refund as taxable income, because they had previously written it off as deduction. You can't take a deduction and when it is returned to you, ignore that fact. That is a free ride, in other words. If you didn't declare it for purposes of a write off, then any refund is not reportable, because you never reported the paying of it as a tax deduction in the first place.

So, if you use the State payment to your benefit (a deduction) in Federal tax filings, you need to report that you got some of it back (report as income), when that happens. If you use the Federal payment in State tax filings (deduction), and you get some of it back, you need to report that as taxable income. If you don't use any amount for deduction purposes, then you don't report any refunds, either.