[BYprodriver]

I did not watch the video but sounds like you upset the balance of the car mid-turn. If downshift to a lower gear that excessively raises rpms when you reengage the clutch, it's known as "engine braking" & has same effect as pulling the hand parking brake.
As you prepare to enter a turn complete all braking & shifting while the car & steering wheel are pointing straight. This allows you to go slower into the turn & faster out, which is the fastest overall strategy & incidentally safer if that's important to you.Get you & your Box out to a autocross where you can practice car control while only risking killing some cones. Boxster is one of the best street vehicles ever made to do what you direct it to do. Unfortunately if you give the wrong directions it follows those also without prejudice.