Apart from the chronology being completely incorrect?
Pochettino did what Cortese wanted, not through obligation, but through instinct. Unfortunately for Southampton, Markus Liebharr, who appointed Cortese, died, and his daughter-and-heir, Katharine, figured the family had spent enough of their fortune on an English football club. With strategy tending towards a breakeven point, Cortese resigned. It was inevitable that Pochettino would follow.