What is the correct method of importing an object with multiple materials from Blender?

After importing an object that has 2 different materials, I'm encountering issues with the UV mapping. One of the materials is appearing different than in blender, as if it was not mapped correctly. I have a temporary workaround, since the texture on one of the materials is really simple and I can do a "Swap UVs", but if I would like to add more detail, that option will not be enough. I'm importing the model by saving the .blend in the assets folder.

That's the way the model looks with swap UV disabled

and this is how it looks in render mode in blender.