I recently pulled the trigger on a used, but like new Elite Direto-XR trainer and love it. It also came with a Trek FX 2 road bike, which has a ten-speed chain (not sure if it’s road or MTB), 10-speed R10 microshift rear derailleur and the trainer has a 12-28T 10-speed Shimano Deore 10-speed cassette on it. The whole setup was tuned up and everything shifts nicely, and I’ve done some rides in Zwift without issue; some of the gears are a bit louder than others, but that difference is minimal at best. No chain slippage/ skipping, either. Some research has concluded that the bike itself was originally sold with an eight-speed cassette/components before the 10-speed conversion, and the trainer did come with a Shimano CS-HG500-10 cassette, which due to some wear/grease on the cassette I can only assume it was at one point on the trainer prior to the Deore. Is it an issue to have the Deore/derailleur for use on the trainer with this road bike?
If its working and giving you no problems then - no, no issue - ride on.
You can go down a huge rabbit hole of different generations of different families of Shimano groupsets - arguing about the different amounts of cable the shifters pull on each change and the min/max capacities of different derailleurs - but yes, there are combinations of kit from different groupsets that work just fine. Enjoy and keep riding.
There is some complexity to this. Setting aside Dura Ace, 6-9 speed Shimano derailleurs all support the same amount of cable pull. 10 speed road same. 10-11 speed MTB Dyna-Sys is different. 11 speed road also different. So it depends on which generation of Deore derailleur you are thinking about using. I’m not sure the noise issue you are experiencing is related to the derailleur though. It could also be a mismatch in the level of wear between the cassette and the chain, or an adjustment issue, or a derailleur hanger alignment issue.
Also 10 speed road Shimano Tigra 4700 has same cable pull has Shimano 11 speed road and is not compatable with other Shimano 10 speed.