Be careful not to caulk it up too much so that the water is 'dammed' up on the J-channel. Do caulk quite a bit on the UNDERside of the channel (at the ends) first, then do the 'visible' seams. Be sure to do the same at the bottom of the window AS WELL AS around your doors.
Geesh, that really stinks! I just can't imagine any more that a Homeowner has to 'inspect' a Pro's work. How can anyone have any confidence in a Contractor. I guess it pays a bit to know at least 'how' the job is done.
Good work, Bob, in 'catching' the cause of this problem. I do hope that's the end of them. My best to ya and hope this helps.
Jay J -Moderator
PS: Have you considered calling the Contractor back and 'sticking around' while they do the fix??! It may mean a day off BUT at least you'll know the job was FINALLY done right ...