This weekend's match at Villa Park pits Mings against his former club.
Asked if Mings has a point to prove against his former employers, Smith said: "No I don't think so. He's quite a level-headed lad anyway. He's played big games in the Premier League for them and some of them were last season.
"Tyrone knew he needed to get out and play football. We enjoyed having Tyrone and he enjoyed being here.
"We took up the opportunity to buy him but I know Eddie (Howe) has said he didn't really want him to leave. But Tyrone knows he has to go and perform for his team."