Yes, you are trying the right thing(s). First of it’s not oil, it’s (muddy) water (where should the oil come from? 
).
And yes, this part is the possible buggy one.
- I think this part works best when playing alone, i.e. use only one controller.
- Moving it is the way to go, but you shouldn’t just stand there.
- When switching characters ensure the action button stays pressed until you have switched to the other one.
This should help for now.