This seems to be the case with my PSR-E433, as well. I rarely use styles, except for the drum rhythm, but I thought I had seen chords display in that area of my screen during various times as I was playing or recording on my keyboard. So, after reading this thread, I tried it on my keyboard, thinking that I might see the chords display if I turn on the split mode, but that didn't happen. I only saw the chords display when I turned on the auto-accompaniment (ACMP) feature, so that just seems to be the way these keyboards are designed.
It will display the notes being played on a musical staff with the auto-accompaniment turned off (not sure if the E413 has this feature or not), but it will not "calculate" and display the chord you're playing unless the auto-accompaniment is turned on.