Tony normally the module is not duplicated but is shared between the websites except if you selected that you want to "copy" the "/modules" directory (that is not recommended).
I don't know what you did to filter the search in this module but for your information, it is alway possible to know inside PHP if you are runing under a slave site or the master and also to know the JMS site ID.
So perhaps you could have a specific setting in your specific module that would use different values depending on the slave site ID.
If you want that we help you develop such module, this is also possible with our billable support that you can order at
www.jms2win.com/en/joomla-multisite?page...35&category_id=1