Inquisitors usually handle major crimes, and are sometimes loaned out to other factions for questioning (e.g. Kel Brezan in Raven Stratagem). Most things like space traffic tickets are handled by lower-level magistrates.

The Rahal will tend to determine guilt/innocence and hand things off to the Vidona for the actual torture, but it's not unheard of for Vidona to take things into their own hands. This is sometimes a bone of contention between the two factions.