How can I auto-deploy my git repo's submodules on push?

Question

I have a PHP Cartridge that is operating normally, except I can't find a straightforward way to get OpenShift to (recursively) push the files for my git submodules when/after it pushes my core repo files.

This seems like it should be a super straightforward and common use-case. Am I overlooking something?

I could probably ssh into my server and pull them manually, but I'd like to automate this completely, so that if I update the submodule's reference in my repo these changes will be reflected when I deploy.