Yes, I think for the personality traits (like the ones created with the Trait Constructor), modders should add the MINIMUM, otherwise the Sims would probably lose the trait if they happen to get switched to the minimum lod (which can happen for unplayed/unhoused Sims for example).
Full Sims are basically played/housed Sims, base Sims are unplayed, and minimum Sims are unplayed/unhoused kept for the family tree (or at least that was the case before the patch)