Whatever dollar amount that you convert that is more than your contribution is taxable income when you do the conversion. It doesn't matter if the increase was from investment gain, bank interest, or this incentive.
Very simple, no extra paperwork. Report the conversion from the 1099-R per the usual methods.
If you have to hold the money longer to qualify for the match, that's a separate problem. But the conversion itself is no different than any other conversion where you have some interest or investment gains.
