It is because your tattoo is named. Your MTL is actually still lower than your tattoo level. Unequip the tat to see what it really is.
Correct, but technically not quite 100% accurate, terminology-wise.
His "effective MTL" is exactly where it's displayed it is (9,080,595), and he can see his "base MTL" when he takes the named tattoo off (around 8,731,341).
Sadly, his "effective tattoo level" (9,434,472) is never displayed anywhere, he can only see his "base tattoo level" (9,071,608).
Your tattoo starts growing as soon as effective MTL >= effective tattoo level, which is the exact same moment your base MTL >= base tattoo level.