How do these work exactly? I believe you're supposed to press the corresponding skill in time with either the sprite animation loop, or the sound cues like a rhythm mini game, but I just don't seem to get it. 

Most of the time I'm better off mashing I feel. Is this the case? Or is there a way to always crit during the juicing mini game?

press the corrosponding button at least 3 or 4 times per second

When I started this game entirely blind, this was what I struggled with for a long time before eventually learning through repeated effort and diagnosing things around how it worked. It's significantly easier now with being able to see the settings for it in keyboard configuration, but as Annuilein said, you press the corresponding key.

Ignore my probably weird key setup, but for example, I had the keys set to 1, 2, 3, 4. I learned that, based on whatever juicing attack I chose, all I had to do was spam the correlating key. I would recommend for your key setup, just to engage juicing, and spam only one key. If it's slow, then reload the save and try another. Assuming your stamina is sufficient, you'll likely win quickly against any normal enemy, making it clear what button you're meant to press.

For example, in my case, I would press 4(Juicing hotkey) (and hold) ->(right arrow key) and then spam 3, which correlates to that action's juicing.

In my experience, I still spam when doing doing it for money and not juicing, and in that case, if you get any wrong inputs, you'll lose out on potential money. Hope this helps c:
*(edit 1) Just to be clear, you must STOP spamming at intervals throughout this job; I have all the options memorized, so I spam, then wait, then continue, etc. If you have sound on, you can hear the wrong inputs, and your customer also becomes upset.

what ever buttons on you keyboard you assign to the first 4 slots of the hotbar, spam those continuously to juice.