Rooney was demoted to the bench against Fulham last month with stories that Ferguson was not happy with his fitness levels.
But Stubbs told the Daily Star Sunday: "Wayne's with the best manager I have ever seen who doesn't suffer any fools. We have seen in the past when he has had top players that if you don't take on board the little kick up the backside, then you are soon out of the door.
"Wayne will know that. No matter who you are, every player tries to push the boundaries every now and then. Deep down, though, Fergie loves Wayne.
"And Wayne looks on Sir Alex as a father figure. There's no problem there. Wayne respects him more than anyone in football.
"As long as Wayne keeps producing on the pitch there's no reason why they will change. It was Sir Alex's way of saying, 'Oi, get your focus back on track'.
"Sir Alex is coming to the end of his managerial career and do you think he wants to go out losing?
"Wayne is twenty-six and at potentially the biggest club in the world. He's been at United eight years and will want to carry on until his early thirties. There's only Wayne who can stop himself from doing that."
The Alan Stubbs Everyman Cancer Appeal was launched to raise awareness of testicular cancer, which he suffered and fought back from.