Tethys provides the Docker containerized version of GeoServer as a convenience, but there is nothing really special about the Docker version versus a version you install manually yourself (though with our latest Docker version, it comes with a bunch of extensions out of the box and the capability to setup a clustered version of it see:
http://docs.tethysplatform.org/en/dev/whats_new.html#geoserver). If you use the Docker container, then the version of GeoServer that is installed is based on what version of Tethys you are running:
< Tethys 1.3.x = GeoServer 2.6.1
Tethys 1.3.x = GeoServer 2.7.0
Tethys 1.4.x (dev) = GeoServer 2.8.2
However, if you upgraded Tethys without upgrading your GeoServer docker (common), then you are probably out of sync. IF YOU DON'T CARE ABOUT THE DATA IN YOUR GEOSERVER, then upgrading the version of GeoServer that corresponds with your Tethys version can be done using:
(tethys) $ tethys docker update -c geoserver
THIS WILL RESULT IN DATA LOSS.
Preserving the data is somewhat tricky, but I outline the process for going from version 2.7.0 to 2.8.2 in the dev documentation:
http://docs.tethysplatform.org/en/dev/software_suite/geoserver.html#migrate-to-new-geoserver-docker It should be a similar process going from 2.6.1 to 2.7.0. One of the features of the GeoServer docker in the dev branch is that we mount a directory from the host machine into the docker container and the geoserver data directory is put in that directory. This gives you direct access to the contents of the docker, on the machine that is running it.
We just made the upgrade to 2.8.2, so we are not likely to upgrade to 2.9 any time soon (they release a little too often for my tastes). You are welcome to try any version of GeoServer that you would like by following their instructions for installation:
http://docs.geoserver.org/latest/en/user/installation/index.html#installation. As you said, Tethys Dataset Services API may not be compatible with versions that aren't officially supported by Tethys, but the REST API has been fairly stable, so I don't anticipate any major issues...