I'm familiar with container functors and older work by Dybjer on categorical models for Wtypes in the extensional theory, but I was looking for some similar semantics in the intensional case.
Unless I've not understood your question correctly (sometimes people mean different things by the distinction between intensional and extensional), then I think the answer is: the semantics for Wtypes in intensional type theory are exactly the same as the semantics for Wtypes in extensional type theory. A model of type theory (comprehension category, category with attributes, et cetera) is essentially just a Grothendieck fibration $p:E\to B$ which comes equipped with certain structure. Being a model of Wtypes just means that $p$ comes equipped with certain extra structure. As I understand it, the difference between intensional and extensional type theory has to do with which axioms are satisfied by the identity types. (In terms of $p$ this is just whether it is equipped with one or another kind of structure for interpreting identity types.) Whether or not you are able to interpret Wtypes is again simply a question of whether $p$ has a further kind of additional structure and is a prior independent of which kind of identity types $p$ is able to interpret. In practical terms, what this means is that the question of whether your model supports the interpretation of Wtypes has everything to do with your fibration $p$ and formulated in this way the question is completely independent of whether the model is intensional or extensional. E.g., if your fibration $p$ comes from something like a class of display maps and you want to interpret Wtypes as initial algebras for polynomial endofunctors, then you will need to verify that these initial algebras land in the class of display maps. 

