When I teleport to a different map, does the time on the original map stop?

Yes and no.

All the creatures are frozen in time while you aren't present. The same applies to natural disasters: There won't be any while you are away, and any ongoing disasters will pause and continue as soon as you return. So you don't need to worry about your other bases while you are away. You will find them in the exact same condition in which you left them.

However, production does not pause. Miners will keep using up their mineral deposits and produce minerals. Processing plants will keep converting resources. Non-regenerative power plants will keep consuming resources. Even harvesters will keep producing resources based on what their average yield was at the moment you left the map.

Unfortunately this can not be exploited if you run out of resources while being attacked. Rift-jumping gets disabled as soon as an attack countdown starts and doesn't get enabled until the attackers have been repelled.