Sallen-key second order bandpass filter low frequency response
A square wave of 200 Hz contains odd harmonics all the way to infinity. The 25th harmonic of 200 Hz is 5 kHz hence you see the band pass filter extracting this harmonic and greatly amplifying it.

Here's a picture of the spectrum of a band pass filter on the 17th harmonic (nearest I could find): -



Picture taken from Acoustics and Psychoacoustics: Introduction to sound - Part 8

So, if you look at the step response of a band pass filter you will see waveforms like this: -



Your circuit (Q = 2) will have a zeta of 0.25 (pretty close the the green trace) and each time the square wave pattern changes you get the step response repeating again and again.

Your interpretation is flawed - a sallen key filter isn't the same as two cascaded 1st order filters because two cascaded filters cannot, by mathematical or practical definition, produce a Q greater than 0.5 and therefore cannot generate decaying sinewave responses as you see.