To rinse is to either 'wash gently with liquid substance', or in this case 'to DO or carry out any act with more than the average effort or speed', or 'to do something fast and efficiently'. Apparently it comes from the old english phrase 'rincier'.
'Core' is to add emphasis, as is done with the music genre 'breakcore'. The music has lots of 'breaks' in it, and the fact it has lots warrants the adding of 'core' to the end of the word.
Warren: 'RINSECORE MAN!'