The only thing that Dave said about June is that he and Stevie will continue recording the album, and hopefully finish it by then. Obviously, that does not mean the album will be released in June, but by then it will be able to go into post-production.
Here is the mention about June in relation to Stevie's album. He mentioned it on a BBC radio show during an interview, and here is the summary of the conversation by someone at a Eurythmics fan site:
"Dave also spoke about working with Stevie Nicks, that 6 tracks are recorded so far and they will try and complete the album in the Summer, and that he is hoping to play live with a “bunch of reprobates”"
http://eurythmics.me.uk/?p=12219
The write-up says in the summer, but in the actual interview, if i remember correctly, he said June would be when they continue with their sessions.