Installed a new replacement chain [Shimano Ultra CN-6701] and rear cassette [Shimano CS-6700] on my commuter bike because the old ones were very worn. Purchased at Seattle flagship store with my bike along for reference. I've done this service previously and it worked for about 2 - 3,000 miles.

The old parts shifted relatively well and indexed OK though worn.
Derailleur hanger appears straight and there's no reason I can think of why it would have got bent in the R/R process. 

New parts won't index or shift properly.

Did some research and it looks to me like the existing 10-speed Tiagra SL 4700 right-hand [rear derailleur] shifter that I had on my bike is incompatible with the new rear drive train bits, because it doesn't index well or shift smoothly across all 10 rear cogs. Running a Shimano 105 RD-5701-gs rear derailleur.

Can you confirm the incompatibility? The logical fix at this point would be to replace the shifter. It's the oldest component at this point with probably 10,000 miles on it. I'll just find a more compatible Shimano 10-speed right-hand shifter, which should be more broadly compatible going forward.

Basically looking for verification that the new drive train parts are incompatible with the Tiagra shifter and that the new, more-compatible shifter should bring things in line.