I’m no janitorial expert, but I’m thinking these things should be rotated 180° with the wide ends lined up with the outside edges of the porcelain fixture, that way you’d get better dribble coverage. Plus another clue making me think they are upside down is that the name of the company that supplies them, Cintas, is written in the lower left at an angle that would be easier to read if the thing was rotated around.
The only thing I can think of is the person who is distributing these things believe they are dual purpose and they not only absorb tee-tee, but thinks that maybe they are for the comfort of the person doing the tee-teeing.