It depends on what you mean by linked but in this response I am going to guess you mean either Duplicate Linked or Duplicate Object and not a linked external asset.
In Blender a Duplicate Linked or Duplicate Object will inherit the materials from the source object. But in Verge3d all of your duplicate linked and duplicate objects are just treated as normal objects not inheriting the materials from one another.
In your case, each object is sharing the same material. You will need to adjust your screen to have the other t-shirt materials assigned to a stand-in object out of the camera view. Then you can use the replace material puzzle to assign the correct t-shirt material to the corresponding mesh.