Running the .VSIX gives us the error “The extension manifest is invalid” on machines that don’t have Visual Studio installed. On one machine that has both TFS 2015 and Visual Studio 2015, the error says "The extension is not installable on any currently installed products.
Double-clicking a VSIX file on a machine that has Visual Studio results in an attempt to install it as an extension to Visual Studio - not TFS. By reusing the file extension, Microsoft unfortunately made it a bit more difficult!
The page on the marketplace mentions that this version doesn’t work with TFS 2015 on premises. There’s a UI issue with the dropdowns in the build tasks that works correctly in VSTS, but it doesn’t work on 2015 premises - even update 3.
There’s a link to a page that gives an alternative download for an extension that should work correctly. In your initial email, you mentioned you are using that on-prem one, so I’m a little confused…
For 2015 on premises, the marketplace download won’t work, so that message is correct as far as I can tell.