Our hotel has offered to buy our tickets for the red green, and possibly blue tours and balloon ride. Is it better to do this or buy through Viator or Tripadvisor?
You definitely should go with a reputable balloon ride operator as there was a fatality and 31 people were injured just last month in Cappadocia from a balloon ride accident.
I am not sure what "red green and possibly blue tours and balloon ride" might be, but as Kenko said you want to go with a reputable and licensed balloon company. There are suggestions in these posts https://search.ricksteves.com/?button=&date_range=2y&filter=Travel+Forum&query=balloon+company+cappadocia
Balloon rides are not inexpensive. If the hotel is offering to pay, I would be concerned they might go on the cheap which could be risky. Ask the hotel who they use for the flight and do some research on the company. FWIW Viator and Tripadvisor are third party vendors, so you might not be able to tell who is flying the balloon. It is best to book directly with the balloon company if you do it on your own.
The hotel isn't necessarily offering to pay. It sounds like they are offering to make travel arrangements for the OP.