Celtics2021 is my go to cap guy here. He seems to have the best knowledge of all of this. But here is the exact language regarding Brown's contract as reported on Spotrac:
Contract Notes:
$4 million likely incentives (plays 65 or more games, team wins 49 or more games and reaches second round of playoffs) [ LTBE = 65 games played + All-Star Game]
$8 million unlikely incentives (MVP, DPOY or one of three All-NBA Teams) (@ChrisHaynes)
2020-21: LTBE: $446,429 (65 games played), ULTBE: $2,232,143
2021-22: LTBE: $482,143 (65 games played), ULTBE: $964,286 + $1,446,428 (All-Star)
2022-23: LTBE: $1,380,952 (65 games played, 2nd Round, Conf Finals), ULTBE: $1,035,714 + $1,553,571 (All-Star)
2023-24: LTBE: $553,573 (65 games played, 2nd Round, Conf Finals), ULTBE: $1,107,143 + $1,660,714 (All-Star)
He played 66 games and we won over 49 games plus reached the second round so he gets the $4 but that incentive was considered "likely" so it was already figured in when we are $358K under the tax.
He was not MVP, DPOY, or an All Star so he did not get the $8M one.
I don't see anything here that says that for this season, if we make the finals or win the title, that there is an additional bonus related to that. It is listed that way for 2022-23 and 2023-24, but not for 2021-22 (this season). Spotrac is not official and may not be fully accurate but this is what I am seeing. The entry for ULTBE for 2021-22 lists two values ($964,286 + $1,446,428) but then lists only one condition (All star) so that may be an incomplete description. If one of those values is triggered by making the finals and the other by all star selection, then we would be over the tax.