The whole house filtration system that you cite is a filter. The specs for this filter suggest that it removes chlorine and pharmaceuticals, so I think it's a carbon filter. It's possibly a good filter (there are variable levels of quality carbon filters) and it sounds like there's a timer that flushes/cleans it (that's convenient) but it is not an RO system. RO systems are very different from filters.
An RO system absorbs and removes dissolved ions (filters don't do that). Whether you need an RO system depends on what ions are dissolved in your water.
- RO systems remove salts and other mineral things like silicates,
lead, and copper (etc.).
- General filters remove debris like grit and clumps of microorganisms.
- Carbon filters can remove organic molecules, like pharmaceuticals,
pesticides, gasoline, urea, and chloramines.
Edit- also, you mentioned that have a water softener, which replaces calcium with sodium. RO systems then remove sodium. Carbon filters don't remove sodium, nor calcium.