I would not suggest using Activiti Explorer with your own UI as Activiti Explorer is a VAADIN application which tightly couples the UI to the backend.Rather, I would suggest you use the activiti-rest project to expose REST endpoints that can be called by your UI implementation.
Another options would be to look at the Activiti 6 Beta 4 implementation as this uses AngularJS as the UI framework rather than VAADIN and decouples the UI from the backend using REST.Hope this helps,
Greg