If you manually upload your .rvt files on the BIM 360 Team website you will not see them inside Revit. To verify this Open Revit > click the Open icon > click on the BIM 360 Team or if you are trying to link in a Revit model click on the Insert Tab > Revit Link > clicking on the External Resources icon.
Solution for working with non-Collaboration for Revit files:
Set up your own storage solution outside of Collaboration for Revit. In order to work with Revit, the path accessed by each individual machine needs to be the same. You could achieve this by doing one of the following:
- Setup a central shared location like you would with a Revit Central file.
- Setup a mapped network drive
- Setup a cloud share like Dropbox
If you are working in Revit 2018.2 there is a new Autodesk desktop Connector that allows you to link non-C4R files that are stored on BIM 360 Team. To read in full click here.