Update (7/25/16): You should be fine with older versions of Report Server and SSMS 2016/Visual Studio 2015/SSDT, if you do these three things:

1. Set the appropriate compatibility level for deployment (TargetServerVersion) in the report project properties.
2. Build the report project before deploying (this may also catch some kinds of errors).
3. Deploy from the build output directory (bin/Debug by default) rather than directly from the source code directory.

Disclaimer: I have not yet tested this, but the built RDL looks OK.

stackoverflow: Can I control the version of new SSDT reports in Visual Studio?

Original post:

I only have time for a quick post at the moment, but be aware that if you take advantage of the latest SSMS 2016/Visual Studio 2015 SSDT releases, they do (at last) incorporate the SSDT-BI designer templates. The VS 2015 Report Designer, however, always upgrades the edited RDL file to the 2016 RDL schema.

The Issue

If you publish to an earlier Report Server version using the VS 2015 Report Designer, with the correct target server version set in the report project, the RDL will be rebuilt (in the appropriate bin directory, rumor has it) with the correct schema.

If, on the other hand, you use a 3rd party tool to publish to a lower RS version, or if you provide your own tool, there is no automatic downgrade and it isn’t going to work unless the tool performs a downgrade.

Resolution

I haven’t had an opportunity to address this issue where I work, and the workaround is to continue to use VS 2013 for RDL editing (and VS 2015 for everything else). If I come across sample code for dealing with this issue I will publish a link here. Otherwise, I will put together a post myself, eventually, when I can.

Reference

MSDN: Upgrade Reports

SSDT-BI November preview (for Visual Studio 2015) fails to deploy through Webservice for correct SSRS version (closed as “by design”)