If Spurs wanted to have Hairston with them, they would have called him up just after his last game and Hairston would have joined the team in LA or Utah.
It looks more than either Hairston wasn't able to play this game (injury, illness, family trouble...) or Spurs needed him quickly for various reasons (player(s) out, trade). Given that we have heard nothing about an injury/trade and that Hairston hasn't been officially called up for the moment, I guess that Hairston wasn't just able to play this game.