I’ll look into this. I don’t have a multisite installation online at the moment so it might take a few days to get to it. I do test the plugin against a multisite install from time to time.
It seems that the issue is that users are not being logged out of subsites when they are logged out of the main site. I think that is something that can be solved with WordPress configuration, but I could be wrong. If you find a way to get this to work on your site, please let us know.