New client requesting use of home/cell phone numbers. Sketchy or legit?

I think you did the right thing. I'm always suspicious of people who don't want to use the rover site for communication. I always route communication with prospective and new clients through the rover message board in the beginning, just so I'll have a record of any details and request info. I will usually text the client my home cell number for the meet and greet, in case they get lost or need to reschedule that day.

I think what you did was okay! Now that Rover provides phone numbers for both text (and calling via the app) you definitely don't need to give someone your personal information until you feel comfortable. I think in general Rover can be confusing to new comers, owners and sitters alike. Prior to the ability to call with my Rover number, I did have a couple a clients request I call them (from my personal line) because they weren't "computer people" and preferred to talk over the phone. Those worked out okay but if someone is that put off by your statements (as your guy seemed) they probably would have difficult clients anyway.

I don't think there is any reason to explain that your Rover number is different than your personal number. My experience has been that the whole thing is transparent.