It's clearly missing the pan. It should sit in a flashing pan. They can be maid out of lead (old school) or some manufacturers make them specifically for their doors. It's pretty simple -
http://jamsill.com
If it was caulking that froze before it fully cured, it was the wrong type of caulking to have used that time of year, regardless, it was installed wrong and has to come out to be fixed. I doubt the manufacturer will honor warranty if they come out for future issues and the jamb bottoms have rotted out, not to mention you'll never keep paint on the bottom of the jams as they will wick water up which then comes out through the paint when the sun hits it. Even if water wasn't leaking into the house (just getting under the door), eventually it would rot our your sub floor and rim joist and you could have water leaking into a finished basement, or whatever is under the door.
I'd threaten to go after him under MGL 93A. Have one if his signs made up on card board with a big red circle and line through it and put it up in your front yard. DON'T just let him empty tube after tube of caulk until it stops leaking. Good luck.
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