The relevant Wikipedia article's photograph for the station illustrates that both platforms can be used, and states that both are used, being connected only by the barrow crossing. Looking up the station on e.g. realtimetrains.com will also show that trains are allocated to both platforms.
The 1972 resignalling notice indicates that Carmarthen Station G.F. operates the points as you say, with the catch points being brought into use at that date, the G.F. being released from Carmarthen Jn. S.B. by an Annett's Key, held in an instrument at the ground frame. However, I can't find any clues as to the slightly unusual placement of the trap points. Notice WW371 of 1972: http://www.s-r-s.org.uk/archivesignals/brwr.php