These fusion categories are all weakly integral, each with an FPdim less than 84, and therefore, they are all weakly group-theoretical by this paper. Consequently, they can all be described using models that are, to varying degrees, derived from finite group theory.
The first fusion ring is recognized as N°3 of rank 6 in this paper, and should have a model from zesting.
For the second one, see the last sentence of this comment by Eric Rowell (with $N=3$):
The other fusion rules could potentially be obtained as a Z2-equivariantization of the near-group categories of type Z/N +(N-1) in the Evans-Gannon notation. Just a guess, but the numerology seems to work out.