Given the title, there’s no time travel involved. The main setting is a Vivarium: a little artificial environment, like Biosphere 2. Assuming this to be true, then obviously for whatever reason, the inhabitants are supposed to be kept ignorant that they aren’t living in the real world, so when somebody from outside is caught they claim to be from the future. (Presumably there’s some Big Problem that the vivarium occupants are being shielded from — high radiation levels after a nuclear war, or some kind of disease, something like that — and that’s what the 3-minute limit really is for.)