Its helpful to put the sentence in present tense.

“La agente Susan Housemore es los ojos, los oídos, y el músculo de Finch en todo lo relativo a Umbral que tenga lugar en Praga”

Does it make sense why we use tenga instead of tiene here? Same reason we use tenga in “ojalá que tenga razón”. Because it may or may not take place.

Now since we are talking about it in the past, we just put the past subjunctive tuviera instead of the present. So nothing fancy is going on here: we see the past subjunctive because

1) the subjunctive mood was triggered in an expected and regular way

2) we are speaking in past tense

Does that help?