My gut feel is that:

If you have a very good team and pitching staff, your short relievers will get the most use.

If you have a weak team or even more meaningful, weak starting pitching, your middle relievers will get the most use.

If you are behind, I think the game tends to use your middle relievers. If you are ahead, it tends to use your short relievers.

This is just a "guess" based on what it seems happens to me.

The manual does say though that:
"Middle Reliever: You must have at least one! These are the relievers who come into the middle of the game or later if your club trails."

So even late in the game if you are trailing your middle reliever is likely to be used instead of your short reliever - at least that is how I read this and it seems to me that is what happens.

But...who knows for sure?