Not particularly used AJAX as such in a viable application yet, but I've taken a look at it; From my point of view, a request is just a request, regardless; You talk about the Front Controller (index.php) so it shouldn't really matter to this architecture what or where the request came from.
If it does, then you'd have to rethink your design is how I see it; The issue you have I think, is how to distinguish the AJAX calls from normal requests? What I do, is to prefix the name of the controller with ajax during my research.
So, instead of this,
I would have this,
Makes little difference, since the URL it's self isn't altered (from what I see of it anyways?), so this is the route that I'm going to take. Why? Well for one, I can at a later date, at AJAX functionality to an already mature application, without the need to alter the application it's self. All I would need to do is to add another class method on the Products controller, and voila?
You of course, need to select a response which may well differ, but have I missed something out? Really, I know there is still a lot of buzz going about this, but it's not that difficult to take account of
If the user has it disabled...