[Shionari]

The apology in question is up on his Instagram account.

The question Is, was It a genuine apology or was he told to Issue It by a given entity?

Will Smith took the joke pretty serious and Is also stubborn by nature, so I'm Inclined to believe the apology wasn't purely via his own volition.

To be completely honest, I have my doubts about the sincerity of the apology as well.
Because the way the situation unfolded makes me think that Will's reaction wasn't all that spontaneous. He most likely knew full well that was he was doing was wrong, and yet he decided to go through with it and do it anyway. That he would experience such a radical change of heart so quickly seems pretty dubious to me.
I suspect Will is just doing what is expected of him at this point. For someone of his position and status to react like that and not issue an apology afterward is unacceptable in the public's opinion. Will is probably just conforming to that, to limit the damage that he has done in the best way he can.