Wait, now I'm confused...

"He contributed twice after tax to an IRA, then rolled $6k into a Roth in May, and $6k into a Roth in December,"

When were the contributions made? "Backdoor" typically means the conversion was right away. It also means Nondeductible contributions to the IRA. And this doesn't identify if there is also other deferred accounts, or basis in them.

"Also does this cure the excess contribution that occurred in the post tax IRA? This IRA is now closed as we set it up only for the back-door."

"Backdoor" is how someone making too much to contribute to Roth (a nondeductible contribution activity) would do the same into a Tradition IRA account and quickly convert that to Roth. But the process still is Conversion, and if there are other Trad IRA accounts, then the Nondeductible amount (which would become Basis) is taken into consideration for pro rata taxes. In other words, "backdoor" is used to mean "nontaxable" but it isn't always true, along with "bypassing the Roth restriction." A common error is thinking Backdoor = "I converted all of one account" but that isn't what the IRS regulations define.

"Problem is that we rolled his IRA's and Roth's to a new firm in August."

Then the Dec activity is in that new Firm's account transactions. And now you point out there are Other Trad IRAs?

"But will the plan administrator will only generate a 1099 showing the withdrawal from the Roth next year, as a 2021 action."

Not if the conversion was in 2020.

You really have the following: Get documentation to sort out what happened for which tax year in which activity year.

If there are other Traditional IRA accounts with balances at the time of these Conversions, that would be pro rata taxable, so make sure this is reported correctly. And this means there is Trad IRA from which to remove "excess." That means the Roth Conversions would be Fine.

You might need to seek out more experienced help and get mentored on this one.

"The question remains how do I treat the 2nd 1099 in his tax return for 2020?"

So, there are 2 for 2020? But that is the money Out. The tax year the contributions apply to will be 5498 money it, and last year's 1040, and the year earlier, would be helpful.