It's considered Excess for the year made for. Example: your Roth client puts into Roth today for 2020, then you do the tax return and they do not qualify. The Excess is for 2020; the Earnings are taxed for 2021.

They don't need to live with it for the rest of their lives, if they Remove the excess. They pay the excess tax until it is removed, and the earnings are taxable when removed.

Did you click the link in that article? The Excess Deferral link goes here:

https://www.irs.gov/retirement-plans/how-much-salary-can-you-defer-if-youre-eligible-for-more-than-o...

That article then has other resources. Including:

https://www.irs.gov/retirement-plans/plan-participant-employee/retirement-topics-what-happens-when-a...