Mobile Kit Pro is intended only for the very small screen of phones. I recommend make your main site skin responsive for tablets on up to jumbo sized displays.
All that redirect page does is set a cookie for the case where the mobile phone user wants to use the main skin instead of the mobile skin or clears the cookie to toggle back to the mobile skin. There is no separate mobile site.
mojoPortal detects phones based on the user agent fragments that can be configured but again a Surface or other tablet is not a phone sized screen and the best solution is to make your main skin responsive for different screen sizes and use the Mobile Skin as it was intended only for phones and optimized for the much smaller screen size and often reduced bandwidth of phones.
One could even make a skin responsive to handle phones on up and it should work ok for small sites with only a few pages. But for larger sites the main advantage of Mobile Kit Pro is the menu can handle any sized site hierarchy and make it easy to navigate for phones. And by using a separate skin for phones the css payload can be reduced to only what is needed for phone sized screens whereas responsive css would contain lots of media queries for screens that are larger than phone size such as tablets on up and that makes the payload larger. Since phones often have less bandwith it is ideal to keep the payload as small as possible.
Hope that helps,