If we go ahead with your premise then don't we end up at a partially absurd notion?

1a. Magistrates can warrant people for aiding criminals outside of towns.
or
1b. Magistrates, per the laws, allow that the Spire has jx over more than cities + spire.
2. Magistrates, then, must have jx over all of Thera, even though they might not be on duty.
3. Magistrates have power to warrant for breaking of laws wherever they have jx, even if they are not on duty, as long as they go back to warrant where they are on duty.
4. Magistrates should be able to warrant for crimes they witness in other cities they don't preside over, which is clearly a no-no of the Spire.

On a maybe side-note, you also mention that an off-duty magistrate would have to "return to his jx" to warrant. I assume you're not referring to the same jx I am, right. Since if you are (and stating its the physical territory that the magistrate has legal authority in), then that's just confusing. That would mean that off-duty magistrates can't warrant people for aiding criminals outside of his city, since he has no jurisdiction.

PS: Thanks for actively responding to comments about the Tribunal. I agree with the notion that Tribunal was boring and the laws ought to be re-visited by its magistrates, regardless of the outcome.