does this apply to all kites with turbo bridles?
Not just turbo bridles. You've described normal behaviorfor most 2 line kites.
To expand a bit:
Nose forward (tow point moved UP) can give you increased lift, straighter tracking and reduced pull. These also result in increased speed, reduced responsiveness to turning input, increased turning radius and difficulty stalling.
Nose back (tow point moved DOWN) can give you easier stalls, more responsive turning, tighter spins. The flip side is more pull, less stability, less lift.
Most kites have a sweet spot which is the best compromise between all these factors. I've found that I tend to find the setting I like for a kite and then rarely, if ever, change it.