To have the world seem to turn upside-down is a feeling that must have been common to mankind for many years, and for at least almost that number of years people have needed to express this feeling.
Topsy-turvy was coined for this purpose over four hundred years ago, and has the literal meaning of “top turned over.”
The first element is just top, to which the suffix -sy was apparently added for euphony.
The second element is based on the now obsolete terve (terve), “to turn,” especially, “to turn over.”
Thus it is seen that topsy-turvy is, just as you probably thought all along, “top turned over.”
