Okay, I have good news and bad news. The good news is I was able to verify some information from the previous home owner.
"The undersink RO is after the whole house filter softener and when it back washes it goes to pond thru 1/4 tubing.
The black hose comes from the whole house softener during back washing automatically on Monday about 2am is default."
So, the RO is plumbed after the house filter/softener. I think the 1/4 inch tube is copper.
I did not know at all about the hose backwashing from the house filter/softener. The system time is off right now, but it does that once a week, currently Friday morning.
I'm thinking I better get both of those lines diverted elsewhere. I'm not that handy and not sure what to do, so I will probably contact a plumber.