IRA Distribution delivered in 2021, counted as 2022

I am looking for an official IRS definition as to when an IRA distribution is considered as made for tax year purposes. I have from multiple reliable sources (including a rep at the same huge US brokerage where this was done) that, if funds are withdrawn and made unavailable on Dec 31, 2021, that date is considered a distribution for tax purposes for that year (whether or not an RMD).
To make things even more definitive, they immediately moved the distributed funds to my taxable brokerage account as available for investment OR for cash withdrawal on that same 12/31/21 date (this was done online).
But, this brokerage reprocessed the transaction a few days later and reckoned the distribution tax year as 2022 (now out several thousands of $ in withholding until 2023). Other implications exist here for the 60-day rollover deadline and for the once per year indirect rollover.
I cannot imagine this is in line with IRS rules but finding a statute or reg explicitly so stating has been a challenge. Any ideas would be appreciated.