We reached Oia by ferry in the morning. There was a bus waiting for us with four name cards. Once all four people arrived, he dropped one family at one city and three others at top of Oia ($30 charge at the end).
Then, some porters, arranged by Rena, took us and our luggage to the cave house which was quite a walk, but not unexpected based on her description. We left the luggage there but the checkin time was at 2 PM so, we had to climb back up and wait till 2 PM. In hindsight, I would have left my family up in the main shopping area till 2 PM and gone with the porters alone. The supermarket is kind of far from the housing area, so take a bunch of water bottles with you when you go to the house.
The cave house was awesome and as pictured in the description. The kitchen and bathroom are kind of narrow, but long and sufficient. The housekeeper is very nice and friendly as well. They have a bunch of cats there too. The house is not too far from Oia Castle, the sunset place. There are some mosquitoes in the area, but the house had a repellent available for use.
We met Rena the next day morning and she was helpful with any questions/recommendations we had. She also told us about the various options we had to travel from Oia to Fira.
Overall a pleasant stay.