Is it possible that the BJT will work in active mode even if emitter base junction is reverse baised?
You have written R2=22 kOhm. In the video R2=2200 Ohm. The latter is ok for active region.

The linked lecture is not exactly crap, but uses a not so common convention. It does not in the beginnig show which are the nodes from which the Thevenin's equivalent is seen. T's equivalent in his calculations have earth as the other terminal. It becomes clear later. Accepting this the result is ok. Vth is negative but causes forward voltage from B to E. Why forward? because Vth is less below zero than -Vee.

If we want to calculate T's equivalent for the voltage divider formed by R1 and R2 and power supplies, all seen between base and -Vee (a) or between base and GND (b), the resulted Vth have plus in the base of the transistor. This is common in all textbooks I have seen. I recommend to allways show in the beginning  which are the nodes of the T's equivalent.