Thank you for your post.
Custom file icons were introduced in FileMaker Pro 14. Therefore, when the file is hosted in FileMaker Server 13, the custom file icon will not appear when viewed with either FileMaker Pro 14 or FileMaker Pro 15. You will need to move the hosted file to FileMaker Server 14 or later to view the custom file icon from the host.
Once you open the file hosted with FileMaker Server 13, it will appear with the custom file icon under "My Solutions", but it still won't appear with the custom icon under the FileMaker Server 13 host.