Should I shorten the prayer or complete it if I pray with a congregation and do not know the intention of the Imam—whether he is a resident or a traveler—and I caught one unit (rak'ah) of the prayer?

If a traveler prays behind a resident, the traveler must complete the prayer. Similarly, if a traveler prays behind someone whose status is unknown (whether resident or traveler), the traveler must complete the prayer. This applies regardless of whether the Imam is completing or shortening the prayer.