MICROSHIFT CS-H081 11-34 cassette does not run smoothly

TL;DR:

On the bike I have a MICROSHIFT CS-H081 11-34 cassette. The same cassette (with the additional spacer) on the trainer is clunky and automagically changes some gears. Do I need additional hardware?

Verbose:

I bought a Triban RC 120, then had an injury and I can't ride on the road yet, so I decided to buy an indoor trainer to both rehab and train seriously. 

I unmounted the cassette from the rear wheel and mounted on the freehub body of the trainer and hoped it would run exactly like on the bike. It does not. Issues on the first gear (34) and the last two or three. I already mounted the spacer as per instruction manual.

Any hint? DO I need to adjustment the rear derailleur or do I need some additional hardware? I'd prefere to not change the setup of the bike, but since it will take some months before riding again, It can be done.