When dinner was over, we moved to the living room.

Literal

Dinner [subject-が] finish-[conditional-と] living-room [to-へ] move-[past-った].

The ~と conditional explicitly marks the automatic sequence — 'as soon as / whenever dinner was done.' Compared with the gentler ~て connector, ~と feels more like an immediate trigger; with past-tense main clauses, it often reads as 'and then.' Japanese gives several ways to string events together without huge meaning changes.