Are you considered served if you find the summons on your door when you come home from vacation?

Yes.  This is called nail and mail service.  Your time runs from when the affidavit is filed with the court.  But, you can call the lawyer to get an extension to answer.

Simply affixing the summons and complaint to your door would not be proper service under NY state law, but it can be part of valid service if the server made several prior unsuccessful attempts to find you, and, after affixing the  papers to your door, mailed you a copy as well.   You should not take a chance on service not having been made, but should defend the suit.  You can find out when service is claimed to have been made by checking the court's docket (look for a document called "affidavit of service") or by calling the plaintiff's attorney.