it will mirror from the border edges so if you only have a border on the x axis and mirror on the y then only then you could get some wierd results ect.
The trick is to keep your vertices on the center axis, you can always select the center line of verts and scale them in the x axis to line them up and then snap them to the center by holding down ctrl + X and middle mouse draging acrose the center line.
I personally would not use the mirror geometry funtion as automatic processes do not always do what you intend.Instead i would duplicate the geometry and then in the channel box scale the geometry -1 in the X ,then under mesh hit combine and finally select the center vertices and merge them individually.