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Oh for heaven's sake, if this is a homework assignment don't go turning in the ramblings of KBK. You do want to stay in the course long enough to finish it, don't you?
The explanation is simple, and has been pointed out here twice. I would suggest redoing the experiment with a single wideband driver or single channel of headphones, and also doing trials at different sound pressure levels. A flat FR transducer is important if you want results reproducible by others, but not if the assignment is only a "neat... look at this" sort of experiment.
Fletcher Munson curves are generalized curves. Specific individuals will have somewhat different curves. Also, by definition the curves show how the human ear (generalized, again) varies in frequency response as a function of SPL. What you will find is that different listeners hear the transition at slightly different frequencies, and also that varying the SPL will result in a given listener hearing the transition at slightly different frequencies.
I suggest the single wideband driver because the presence of crossovers smearing a square wave might have some effect on the perceived transition frequency, and that would be interesting to note because the total energy in each harmonic would not be changed by the crossover. How the phase relationship between harmonic components of the signal affect the transition would be very interesting, and demonstrate an understanding of the phenomenon that your professor probably wouldn't expect. And while wideband drivers do have a limited frequency response, you have already established that the transition effect is high enough in frequency to be within the operating range of good widebands. If you really wanted to do a nice study (not sure how important the assignment is), insert a variable all-pass circuit in line that has an Fc near the transition frequency and try to isolate the role of harmonic phase relationships, or document the absence thereof.
Finally, follow up by examining published F-M curves (and the more recent ones... don't recall the name) and compare the perceived loudness of the fundamental and the second harmonic at the SPL corresponding to the proportion of the signal each contrubutes to a square wave at the SPL you used to test. See if those perceived loudness curves for the two frequency components happen to cross at the transition frequency you observed (in a given trial)....
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