With Tiagra 4700 shifters, 10 speed cassette and chain already fitted, I would have looked to fit a Tiagra 4700 RD, but that's just me.
The article that Aaron linked to shows that the Ultegra 8000 RD can be used with the Tiagra shifters and ten speed set up. It's not something that Shimano recommend, but that doesn't necessarily mean that it can not be made to work.
I have Tiagra 4700 on my Trek Emonda. We have a turbo fitted with an 11 speed cassette. The other half's bike is all Ultegra and it works perfectly.
I've been unable to make my Tiagra 4700 bike work on the turbo without the same symptoms as Aaron described. I have to swap the cassette over to 10 speed to get it to work (a bit of a faff), so I'm looking forward to hearing from Aaron to see what I can learn.