Suppose I have to make the following things:
Its not incorrect but you are creating double work. You are creating web services in PHP to service the android client call this API1 then you are creating a Vaadin based web site which also acts as an API call it API2.
Two API's in different frameworks to maintain which is just adding more maintenance and complexity. If the web site mimics the android application you will essentially be duplicating the code.
Or if you want that in pictures:
Create a web-services API that will be used by Vaddin and the Android application. This will eliminate the double work. If you create the Web-services using REST or SOAP you will be able to reuse those services across both front end application. Now when you grow the application i.e. you want to add iPhone you can simply consume the same services.
Or in pictures:
Hope that makes sense.