The vent that was installed under my kitchen sink has started to overflow water onto my floor when I drain the sink. I didn't like the idea of this type of vent in the first place, but the plumber convinced me that it would work fine and would keep me from having more than one vent stack coming out of the house.

Why is this happening and can it be fixed?

Your plumber probably installed a cheaper AAV and now it's gone bad. Replace with a Studor Vent, (see image) Good luck, Tom