Doomfist’s Jump Punch is a Doomfist ‘technique’. When Rocket Punching, press the jump button at the end of your punch, or any time during the punch (but at the end allows you to gain maximum distance). This allows you to fly an extra ten meters. It is similar to Genji’s Ledge Dash ‘technique’, which was removed, as it allows Doomfist to gain unintended mobility that he shouldn’t have- he was nerfed down from a 30m rocket punch for a reason.
The Turn Punch is similar to the Jump Punch. When Rocket Punching, turn in a direction and press the Jump button at the end of your rocket punch in order to make a quick turn, often at a 90 degree angle. This grants Doomfist unnecessary mobility which he, again, isn’t intended to have.