Postbox is a fork of the Thunderbird project that is popular with some users. ExQuilla does not work with Postbox, partly because Postbox (unlike Thunderbird) is a closed-source application. ExQuilla is a binary addon that requires access to the source of the underlying application to work, which is not available for Postbox at this time.
For ExQuilla to work with Postbox would require a formal agreement between myself (MesQuilla) and the company that owns Postbox for access to the source so that ExQuilla could be compiled with Postbox, and necessary modifications made. Those modifications would not be trivial, as Postbox is a fairly old fork of Thunderbird. At the moment, I am not convinced that there is sufficient demand for a Postbox version of ExQuilla to justify the business effort of negotiating an agreement with Postbox, along with the technical effort to adapt to their old code. So there are no current plans to provide a version of ExQuilla for Postbox.