I guess you failed to correct the unit list.
In the editor, go to units, then select each UU and for each of these UUs, check the list of civilizations (roughly it is a column in the center). At the moment they are probably all selected. Just click on the civ you want able to build this UU. When it is the only civ highlighted, you have got a real UU that only that civ will be able to build.
OK ?
By the way, welcome to Civfanatics !