Snape's wand did not change allegiance when Harry, Ron, and Hermione knocked him out

It looks like Snape's wand did not change allegiance when Harry, Ron, Hermione knocked him unconscious with their simultaneous Expelliarmus.

Prisoner of Azhaban chapter The servant of Lord Voldermort

“SILENCE! I WILL NOT BE SPOKEN TO LIKE THAT!” Snape shrieked, looking madder than ever. “Like father, like son, Potter! I have just saved your neck; you should be thanking me on bended knee! You would have been well served if he’d killed you! You’d have died like your father, too arrogant to believe you might be mistaken in Black — now get out of the way, or I will make you. GET OUT OF THE WAY, POTTER!”

Harry made up his mind in a split second. Before Snape could take even one step toward him, he had raised his wand.

“Expelliarmus!” he yelled — except that his wasn’t the only voice that shouted. There was a blast that made the door rattle on its hinges; Snape was lifted off his feet and slammed into the wall, then slid down it to the floor, a trickle of blood oozing from under his hair. He had been knocked out.

Harry looked around. Both Ron and Hermione had tried to disarm Snape at exactly the same moment. Snape’s wand soared in a high arc and landed on the bed next to Crookshanks.

Does this mean that Snape's wand (or any wand) will not change allegiance if two or more wizards disarm its master, or is there some other wandlore rule at work?