Each gene is picked per trait, Class, Sub Class, Profession, etc. and there is a 50/50 chance that the summoned hero will have that dominant gene.

Current chances per trait. D - 75%, R1 - 18.75%, R2- 4.6875%, R3 - 1.5625%

If both the summoner and assistant pick classes with a chance for mutation there is a 25% chance of mutation. I.E. Pirate + Monk -> Ninja

For Sage + Dragoon -> Dread Knight this is halved to 12.5%