The only references anywhere in Trek to a Starfleet employee getting paid are from TOS. In "The Doomsday Machine", Scotty receives a compliment from his CO:
Kirk: "Scotty, you've just earned your pay for the week."
In "Who Mourns for Adonais", it's Chekov who gets the praise:
Kirk: "Mister Chekov, I think you've earned your pay for the week."
The formulaic expression may well be a mere saying in the 23rd century, unrelated to any actual payment. Surely sayings about money will survive money itself by 200-300 years... By Jove, old Roman religions are still going strong almost two thousand years after their factual demise!