I read about absorption chillers and found out that the water is evaporated/boiled off at the generator.

Water boils over at about 3.7 Celsius in the near-vacuum conditions in the generator. Now the boiling point is also the condensing point! But when this same water condenses at 35 Celsius in the condenser despite the pressure being the same near-vacuum (or is it?), it sends my brain to physics hell.

The only explanation my pea-brain can think of is that the steam itself creates pressure that sort of increases... I hate to say it... its own boiling (thus condensing) point. And so now it condenses at 35 rather than 3 Celsius. Does this even make sense to you?