There are two sub-questions here.
1. Is the same timeout T set for every instance of service X making request A to service Z, or is a timeout chosen at runtime?
2. How is the static (or dynamic) timeout value chosen?
As a clarification, this is more of a poll to understand what people are actually doing, rather than a request for recommendation on what I should do. If you are willing to state which company you work for, I would be extra appreciative!
What can the service deliver?
If you need it faster than it can deliver... then setting your timeouts/paging/whatever to that point will just bring you pain and suffering.
I think you'll find a lot of people just say "what's p99 right now", add a little to it so "it won't page me", and leave it there.
Actually driving down p99... is not nearly common enough.