Is it permissible to have exposed mains conductors in holiday lights?
You are correct in assuming there should not be any live connections exposed in any situation. I suppose it should be said that this is a dangerous situation and could be fixed fairly easy with a set of wire cutters and some appropriate wire nuts. So call the installer and see if they want to make the repair. If they give you any static I would report it to the AHJ in you area and let them deal with it.

Regardless I would not recommend you turn these lights on until a repair was made. As I said before this is a potential fire and shock hazard.