We investigate the quantum dynamics and statistics of an interesting system of the double-well Bose-Einstein condensates in the presence of a coherent photo-association process occurring in one of the two wells. Through the analytical solutions of a simplified model of the atom-molecule condensate, our results show the important impact of initial state preparations on the atomic coherence, especially the different squeezing behaviour for the case of photo-association via left-well atoms tunnelling from initial right-well atomic condensate, which holds the promise to be observed in the present laboratory.