In my view you only have to worry about what your fingers are doing if you lack technique. And technique is developed through long hours of practice exercises and studies designed to improve facility. Once facility is achieved then any rhythm can be played. Same with golf?
It makes sense on the face of it but two of the greatest classical pianists ever, Richter and Argerich, did not even practice scales. They woodshedded for sure but in the context of the rhythmic framework of pieces, songs. There's a theory that if you practice scales minus a rhythm or a beat you'll never achieve real expertise or mastery. Daniel Levitan has written books on the brain and music, he talks about a neurological concept called "chunking". When you play in time with accents it gives something like a rhythmic clothesline to hang the music on, the brain is able to read whole groups of notes as a single "chunk" then string these chunks together. This is exactly how an Oscar Peterson does it, his brain is reading whole groups of notes at once whereas the mere mortal is plodding along one note at a time. In the context of an expert golf swing versus a poor golf swing, I think something similar is going on. By their writings, great players like Nicklaus and Jones were acutely aware of everything they were doing in their golf swings, in tournament play Nicklaus would try to do five or six different things in a single swing. I think the great player's brain experiences the swing differently, it's somehow driven by their fine sense of rhythm and timing. A sportswriter once observed, of Rod Carew, that he looks like has more time to hit the ball than other hitters. That kind of thing.