The ReleaseManager extension is actually only intended to be used to "bundle" a group of Tridion items for a release. The way that it actually works is that it stores all items added to the release in an XML file which is maintained on the filesystem (I've also seen it adapted to be stored in AppData). When you use the ReleaseManager extension to generate the export file, it generates a Content-Porter friendly export XML file which tells Content Porter which files should be exported.
On the subsequent server, you actually just use Content Porter and import the exported zip just as you would any typical release. You can have ReleaseManager installed on this CM as well, however none of your releases will be added to it etc, and would only really serve the purpose of generating releases to be moved into the next environment.
I would recommend you do a bit of reading around Tridion Bundles (introduced in 2013). These are an organizational item similar to Virtual Folders which allow you to group CM items, and can be used similar to ReleaseManager to group a release. You can actually Content Port a bundle as well, so it saves you from having to install a third-party extension, and keeps your releases managed in the Content Managers native interface.