Hi!
When material is applied on the top level group the UV mapping is rendered differently in Enscape than in Sketchup. This is annoying since I often apply material to top level group for example for wall pictures where I want to retain the frame materials, and only change the picture itself.
If you just got and explode group, and then explode just group where a picture is, Enscape will show correct tiling for that texture.
After that, I regrouped it all again and it works well, I tested with ThruPaint to change the texture and it renders correctly.
I guess that is DC, I use SU2020 and when I scale it with scale tool it breaks badly so I can not test it as DC, and scaling that DC could create texture problems, but I am not proficient in DC so I can´t give any advice on that.
Hey jure , thanks for your patience. 
Unfortunately the Sketchup API gives us false/incorrect UV coordinates unless you have a textured material applied to the surface directly. If you do not change the UVs manually (or with other plugins), then these incorrect coordinates happen to be correct, but if the you change the UV coordinates somehow with only a texture applied on the group/component level, we can't read the correct UVs via the API.
So in the end our hands are tied from a technical standpoint I'm afraid, perhaps the advice from namim3d will be helpful to you know.