You can do the presses very fast. With some combos, like Human Smoke's 3 hit popup and Shang's punch->kick combo, you MUST do them fast.
The specific rule is, you have to press the button for the next hit of the combo during the current hit of the combo. Kung Lao's combo starts with HP, LP, HP, LP. If you just press the HP and it hits, it does the first hit, holds for a couple of frames, and then recovers. You have to press the next hit after the current move has started but before it begins to recover.
With Shang's combo, the second hit has so many frames of animation that you really have to press the button for the second hit before the first hit connects, otherwise they will recover before the second hit connects.