You just never know. But the risk of inhaling asbestos from old tile is much less than from something like pipe insulation. Very little asbestos was probably released unless they used a saw on it (or a belt sander!)
My advice is to put on a respirator and wipe the area with wet rags.
I wouldn't lose a lot of sleep over it. Do what you can to mitigate the potential dangers - People messed with this stuff for years before they realized it was dangerous. (And not everyone who came in contact with it got cancer.)
There's always a chance, but it doesn't sound like you would have a lot of particles floating around.