I have a direct mount TACX trainer, the cassette on the trainer is a different gear range than the cassette on my wheel. Does having the different gear range on the trainer require a derailleur adjustment? If so, that might explain why shifting and smoothness is so poor on the trainer. Otherwise I may have setup my trainer with the wrong axle spacers which could be the cause of poor shifting and smoothness on trainer.
BTW, I bought refurb 4k appletv for Zwifting and it is awesome!
Mine is always just a bit off. Seems like I need to turn the barrel adjuster just a click or two between bike and trainer. Never do. Also, shifting on the trainer will always be a bit harsh as there's seldom any real coasting or easy pedaling.
As for the different cog sizes, maybe you need to adjust the b-screw?