I'm fairly new to using all three components mentioned in the topic.
I've tried searching for a way to configure it the way I want, but so far, there's no joy.
I've installed the Mylyn-Redmine connector, and it seems to work fine.
In order for Redmine to be aware that a git commit is related to it, the commit message needs to the sentence 'refs xxx' where xxx is the issue number in Redmine.
Since Mylyn can link a change-set of files per task, I was hoping that it could inject that sentence in the commit dialog so that we won't need to add it manually.
I assume you use EGit, then you have to install the EGit-Mylyn-Plugin (also in the EGit-updatesite http://download.eclipse.org/egit/updates). This plugin contains the functionality for the commit message.