The Responsive Menu plugin doesn’t show or hide the Responsive Menu based upon the User Agent or Device being used specifically (iPhone, Android etc.) but rather the size of the current browser window.
This is done consciously to enable it to work correctly across as many devices as possible and to not restrict it to specific mobile/tablets etc.
With this in mind we need to set a point at which the Responsive Menu begins to show and this can be anything you want it to be (it also enables you to use it as your main/only menu if required) and adds greater flexibility.
If you do want to target specific devices then you can use their pixel display widths to target these, otherwise its best to change this value and see what works best on your site. Try changing this value on your site, refreshing your browser and resizing. Doing this multiple times will help you decide what works best for your site.
For example, this site is set to 1050px and this is because this is the point at which my main menu no longer fits on one line in a browser window.