Yes, you'll need to include Form 1040-X to correct your 2020 tax return to include the $12k as income.
Now that I think about it some more, if you made no intentional regular traditional IRA contribution for 2020 (or at least less than the limit), only the portion that exceeded the amount that you were eligible to contribute for 2020 was an excess traditional IRA contribution. That may alter the split of the $72k. You'll add the $12k to whatever regular intentional traditional IRA contribution you made for 2020 and 2020 TurboTax will calculate the actual amount that was excess. (You'll probably end up with the permissible amount being a nondeductible traditional IRA contribution, but it will reduce the amount that is subject to the 6% excess-contribution penalty on your 2020 Form 5329. However, it may be a bit of a nuisance to have to deal with basis in nondeductible traditional IRA contributions until you no longer have any money in traditional IRAs.) It's this actual amount of excess that you'll report on the split 2021 Form 1099-R in 2021 TurboTax.
To split the 2021 Form 1099-R, you'll enter two Forms 1099-R that are identical except for the amounts in boxes 1 and 2a as I described previously.
Yes, it would have been better if the employer caught the problem a bit earlier in the year so that the distribution could be made before the due date of your 2020 tax return, including extensions.
