19excellent question and an equally excellent solution ! hats off to you guys,,,even i was stuck in it at some point....the point that one of the starting materials could itself act as the medium(solvent) was surely fantastic and ad-hoc !
6 Answers
1is it some sort of nucleophilic addition? what is that bond with S (methyl)??
1actually , due to EWG nature of S=O group , bond cleavage takes place.then following reaction takes place. 
191thnx organic and eure. i too realised it when i read about the wittig reaction.this reaction uses ylides ( compounds having opposite charges on adjacent compounds , but all atoms hv complete octet).according to that solution would hv been :
but then i realised that this product is obtained when phosphonium ylide is used. but the one used here hs a highly EWG group , thus the above reaction doesn't happen