Sorry but its not really that much of a lottery for them... If you're a trained FAY then you'll do Y and you'll usually be assigned to the rear of the aircraft by your purser before the flight.
If youve done your FJ training you'll most likely end up in J. Usually their roster gets assigned so that there are sufficient FAY's and FJ's on the plane and it shouldn't be too much of a lottery of where the crew will be working.
This is not the system I'm familiar with at CX. Take a BC...given the vast majority of CX BC crew cohort is trained to work J class, with the exception of perhaps sales team members doing Y3 (duty free) who are a bit exceptional in that they are almost always assigned the same position, it certainly doesn't hold that "you'll most likely end up in J". In fact, the ratio hovers around ~30% for J-class eligible BCs working J. Even a "senior" BC who might be 5-7 years into their tenure, and thus soon-to-be-eligible for FP training (assuming they didn't do a fast track to purser). Just due to the way the #s work out, those BC's - including "senior" ones - usually work in Y, especially on a plane like 77G where J class is smaller so there isn't an additional BC position in the J cabin (vs 77H).
And for right or wrong, the FAs I'm familiar with certainly complain about working Y in 77G. And it appears to be the aircraft with the single largest disparity between Y vs J assignments. They may not earn yours or anyone's sympathy around here, but that's just the reality of it.