I used RO water back when I kept reef aquariums and I had an RO unit, because pure water is an absolute necessity for reef aquariums. i eventually gave up the aquariums, then my RO unit broke, so I just switched to city water for my plants. Noticed no ill effects, and I still use city water to this day, so I think that should be your plan B until you get more rain water.
Have to admit plants do respond to rain water better than tap water. I use RO water in a pinch back to tap water
Not sure ------ I think it could possibly be due to fertilising and mag/cal schedule too. They say the rain water can contain nitrates etc ... well, much more than in tap water.
So if the orchid doesn't get adequate nutrients already, then they could respond visibly well when rain water comes along.