Effect of negative voltage at NPN transistor base (interesting example)
It doesn't turn on when there is a negative voltage at its base, it turns off.  The output "Sat_Test" also goes high when QS1 base goes high enough to cause the emitter voltage and collector voltage to get close to the +5V rail. It also goes high when the base goes close enough to the negative rail to cause the current in RS2 (and also RS1) to drop to a low level and thus allow the output voltage to rise.

The output is only low for a region around zero volts where there is enough current flowing through RS2 (and therefore RS1) to bring the output down to about 1V.