Yes, that is correct.
The federal tax withheld can only be applied to that tax year.
You could have applied the "refund" to the following year.
So in your case, you took the distribution and paid what you hoped would be the full tax (20%) in 2020.
BUT when it came to filing the return for 2020, you only claimed 1/3 the income, but still claimed 100% of the tax you paid, so you received a large refund of that tax withheld.
The next two years you continue to report 1/3 the income, but the tax withheld has already bee refunded, so the original tax paid is not reported anymore.
Again, you could have applied (or forwarded) the refund to the next year knowing you would have this income to report, or made estimated tax payments. At this point, you can make estimated tax payments for the tax you will owe for the distribution you will need to claim on your 2022 tax return. You also have the option to have additional tax withheld from your wages if you are still working.
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