If I understand what you're asking, and these are still fresh water fish we are talking about, then the bottom line is you cannot use only RO water, no matter how gradually you change it over. And I'm curious why you'd want to do that anyway, considering the cost and effort.
If for some reason you really wanted to, you CAN remineralize RO water with a product designed for the purpose.. I think Kent makes one.. another would be Salty shrimp. Mainly used by shrimp keepers, as you might guess from the name. That would be an expense & you have to mix up the change water and it's remineralizing product ahead of time, to have it ready for changes.
Reef keeping is quite different. You start with pure water, RO or DI, and add marine salt mix until it's at the right level. One big reason for this is that tap water has varying levels of TDS.. that means total dissolved solids. The solids are composed of many things, including metals & some toxins at varying levels that are supposed to be safe for us humans.
I've heard that many reef keepers use a TDS meter to make sure the water they start with measures ZERO TDS, either DI or RO. Then they can use the TDS meter to determine when the salt mix is right. They also use other measuring devices to ensure salinity is correct. I am NOT an experienced reef keeper. I've never kept salt tanks, but I am planning to try to raise shrimp larvae that need brackish water, so I have been looking into salt water lately, to learn how I'll have to do it.
Salt water for water changes has to be mixed a day or two ahead of time and left with an airstone or pump running to thoroughly mix it up and aerate it. I think something similar is needed when you mix up remineralizing products with RO to use it for fresh water. This is more often done by shrimp keepers who keep crystal and Bee shrimps. They're more sensitive to many things, and need fairly acidic pH, and a KH that's very low, if not zero.
If you have fish that like acidic, soft water, then using a carefully balanced mixture of RO and tap can give you the right parameters for those fish. But you'd test to make sure you had the proportions correct, and periodically test to make sure they are still the same, because water from the tap can change with rains or drought and other events.
Fish that do not need acidic, soft water and many, if not most of the inverts, such as snails, need a KH [ calcium hardness ] that's at least 4, and DH [ general hardness] that's at least 6, if memory serves me and a suitable pH level, to be able to osmoregulate properly or grow healthy shells, respectively. These mineral levels also help to keep your pH stable. Having stable parameters is the single best thing you can do for your fish no matter what kind they are.
I'd suggest you do some reading on aquarium water chemistry. It isn't the simplest topic but the very basics are not that difficult. Get a KH & GH test, that will tell you just how hard your water is, and how much calcium it has.
And if your fish are healthy in your tap water now, imagine how they'd fare in water that had zero minerals in it ? I'm not sure what happens.. it's not something I ever thought to check on, but I suspect the fish would quickly die. Possibly swell up 'til the internal pressure kills them.. If anyone knows for sure what happens, I'd be interested to hear it.
There is a disease called dropsy which some fish can get, and they do swell up, so much that their scales are pushed up until the fish looks like a pinecone. The eyes pop as well. The fish dies if you have not already euthanized it. These fish have lost the ability to regulate their internal body pressure, so they just keep swelling 'til the pressure on their organs kills them.
Tap water, though it's not pure, is normally somewhat hard and somewhat alkaline. It can differ from place to place and if you are on well water it can be very different indeed, but most city water is treated so that when it reaches your tap, it's pH is usually over 7 and the water itself is somewhat hard. Locally, our water is very hard, with a pH up to 7.8, sometimes 8. Despite that, most fish live in this water very well, including most that prefer it softer and acidic too. Those that really need it more acidic and soft, well, those keepers have to find ways to keep their water acidic and soft, which may be achieved by mixing tap and RO to the right balance.