ozonated water for rinse cycle in cleaning vinyl

Your water is totally generic. The several processes are all there are for 'purified water'. So it can be either or and reverse osmosis is the best as it removes the most stuff: though a variety of posts have mentioned that ultrapure water can have problems (I tend to not worry about those problems, I just mention it for completeness)
So reverse osmosis OR distillation: Distilled water for sale cheap is usually steam distilled (from some power plant, or or other industrial plant with steam as a by-product, cheap steam water is ALWAYS from an industrial plant as waste) and most often has a lot of iron in it, then filtered, ozonated. Ozonated means the water was treated with ozone. O3 which gets bubbled through the water, so some dissolved O3 will remain? BUT your water may not have had that treatment anyway..
I guess your water is 'treated'. Which treatment is a guess, as the bottle says basically ANY treatment might have been used.
Good luck.
Personally I would skip using such an unknown. Especially because the next batch may use a different means of 'purification'.
If you want ONE form of clean water, try Pepsi brands' "Aquafina" it is only using Reverse Osmosis and that is a good process, leaving very clean water.

No problem, ozonated water is part of process to kill bacteria. I think UV light does the conversion.

Should you wish to go with even more pure water, lab grade is sold via internet and I've had the best results with NERL Reagent grade.

Both responses are slightly off.

The water has been treated by passing O3 through it from an ozone generator (basically an electrical arc in air). The half life of ozone in water is quite short so no dissolved ozone will remain.

The purpose of the treatment is to kill any bugs in the water before it is packaged.

One problem with ozonation is that if there is any appreciable bromine in the water it will react with the ozone to form bromate which is a health hazard. If the water was adequately deionised in the first place this is not a concern.

Several of my neighbors are scientists and research Dr's and all of their labs have the equipment to purify water to "laboratory" grade. They have explained the process at length, although I don't remember the particulars, and it is a much different product than anything you can buy in a store.

I rotate who I ask, but they all are great about getting me a few quarts at a time to clean my vinyl. The hardest part is getting a container sterile enough to put it in. I give the the bottle, and they sterilize it again prior to putting the water into it.