What the custodian probably meant is either it was too late to make the distribution on December 29th but would instead be processed on December 30th, or that the distribution request would not be processed until January 2nd or 3rd. Regardless, the distribution you received is still officially your 2022 RMD, although it might be a late-taken RMD. (RMDs are normal distributions, they are just ineligible for rollover and distributions are RMD until your RMD has been satisfied.)
If the distribution was processed in 2022 and appears on a 2022 Form 1099-R, report it as usual.
If the distribution was instead processed in 2023 and will be reported on a 2023 Form 1099-R, whether or not you must file Form 5329 to request a waiver of the excess accumulation penalty depends on whether or not 2022 was the first year for which you were required to take an RMD. If so, no Form 5329 is needed. Tell TurboTax you were not required to take this RMD in 2022. If you were first required to take an RMD for 2021 or earlier, your 2022 tax return needs to include Form 5329 to request the waiver of the penalty. The distribution made in 2023 will be taxable on your 2023 tax return along with your 2023 RMD..
