ScanGauge needs to update their max SoC equation, as it definitely doesn't charge that high, it is only charging to around 85% if what you are telling me is correct for full charge voltage of around 4.05 V, as I have pointed out before you can't take 4.05/4.20 (96.4%) as the relationship isn't linear and has a non zero intercept, meaning an SoC of 0% corresponds to around 2.7 to 3 V.
My point here is that with the car at 100% charge it has plenty of room to accept at least a small amount of charge as the SoC is still only around 85%, but regen braking can be on order of 50 kW, so they might figure DC fast charging at 85% will shorten the battery life or maybe could cause issue if not all cells have finished balancing (although they shouldn't be far off from each other).
I think you are right that the engine is being started to deal with the excess regen energy, especially immediately after charging (maybe more heat in system, slightly higher battery voltages, etc).
Edit: I re-read your post and it is interesting the charge is still going up, maybe simply a bug that it starts the engine? Or maybe it is able to deal with some excess power in extreme regen cases (like you live on top of a mountain), so it starts the engine preemptively?