There are 2 situations here.
1. Plugin is already installed before setting up multisite. (I am following this)
2. Plugin is installed after setting up the multisite. (Probably you are following this)
In first case, while setting up multisite, the system creates additional set of tables as per the existing system. In this case since plugin is already installed, the additional tables (including the plugin table) for the subsites are automatically created. So in this case the plugin works without any issue.
In second case, since multisite is already set up and then the plugin is installed, the plugin does not create the tables for the subsites. As a result, the plguin functionality works perfectly on main site where as on the subsites it does not work (since there is no corresponding table for this subsite).
I am modifying the plugin code to make it multisite compatible. I will inform here once done. I appreciate your patience.