JEMH is compatible with all versions of JIRA Server since 5.0, and JIRA Data Center (JIRA 6.3+). At points, API breaks occur which mean 'new' features only then appear in 'the next' release. This does not mean earlier versions are not supported, they are. If you have problems or locate bugs, and have active maintenance, support and fixes will be forthcoming! If you want the new features you will have to upgrade, maintenance does not include backporting new features which can incur significant time and/or involve complications.
For current compatibility, lookup you JIRA Server version range in the published JEMH releases:
From time to time, snapshot releases may be made available, these builds are clearly identified by version, and on the welcome screen. Installing these versions is only possible by uploading through Manage Add-Ons, however, once a manually installed version has been uploaded, JIRA will not 'automate' updates to new versions from Marketplace, you'll need to uninstall JEMH and find it again, to get back on the auto-upgrading path. Snapshot builds are not supported and will never be a basis for future support, only actually released versions are supported.