Just wanted to add a quick note... my little boy who is now 3 went though some bouts with constipation in his 2's, and the ONLY way I could get him to go, was to sit for a while in a really warm, soapy bath... so I feel pretty sure your baby's body is just reacting to the relaxing of his muscles, like others have said. I know it is an inconvenience, but boy was it a relief of an inconvenience for us! Try to look at the bright side... at least your little one goes easily!
As for putting the potty next to the tub and trying to redirect your son when you notice him starting probably isn't a bad idea to try. My cousin who has a son 2 weeks younger than my son had him COMPLETELY potty trained by 18 months. Your son may be easy to potty train if he has predictable bowel movements... just a thought. HOWEVER, if he isn't ready, don't sweat that either. Best to let them do it when they are ready, with your occasional attempts to coach him in the right direction. My son has only been potty trained for both pee and poop for the last few months... to each, his own, I suppose!
Good luck to you both!