In modern Reggae terms I don't think there is an agreement but they would defently pay royalties. Most of the best and well known riddims will come from Reggae golden eara. Back in the day it was a bit of a free for all! Check out Jamaica's first ever feature film, staring Jimmy Cliff, 'The Harder They Come' and I would also recommend 'Studio 17: The Lost Reggae Tapes' a documentary that gives some insight on how Studios operated back in the day.
The Harder They Come - https://www.youtube.com/watch?v=L6jXGrSbQMs&feature=emb_logo
Info on Studio 17: The Lost Reggae Tapes: https://www.bbc.co.uk/programmes/m00095ky
Edit: I forgot to mention there is a very interesting part of the above Document that shows how the artists Lord Creator (after becoming very famous) fell on hard times and it was only until the 1989 when UB40 covered his hit Kingston Town he received any royalties for that and other songs that were due to him.