What constitues "module support"; what are the metadata files; what are the pitfalls even when those files exists?

I have a large project that looks like this:

( http://www.javahotchocolate.com/notes/images/nifi-pipeline-project.png )

The modules all look more or less like surveys which I expanded for visibility here. All files are committed in version control. All works perfectly (running/debugging tests, etc.). However, when cloning then accessing the project via IntelliJ IDEA from another host, the module settings do not appear, i.e.: bolded modules, colored subdirectories according to roles, etc. context menus don't include running/debugging tests, and the module settings (File -> Project Structure -> Modules, etc.) are blank as if no modules existed. I'm really sure I haven't neglected committing anything to version control (.idea subdirectories, .iml files) and yet, while what I get back out when I clone from another host is everything I expect, the IDEA project just isn't set up with modules.

I rather expect that I have done something wrong, perhaps when setting one of the (sub) modules up from existing code ( belonging to a colleague using Eclipse), but probably also when setting up the other modules new myself in IntelliJ. What might I have done wrong?

Note, I haven't experienced this problem with other, IDEA projects that don't have (sub) modules.