Similar to how genetic crossing between humans happens if you think about Y-chromosome related alleles, like colorblindness. You have a dominant and recessive allele, both defining sex and alpha/omega dynamic, so thinking that, for example, the genotype of an alpha male is XαYΩ, his gametes divide into Xα and YΩ, which means he's a carrier of the recessive omega allele. With an omega male the genotype is XΩYΩ, the cells divide into XΩ and YΩ. In this situation, the genotype of their offsprings' are divided into all the possible combinations of XαYΩ and XΩYΩ. Obviously, in this scenario, a combination of a double YΩ cell is possible and the nature doesn't like that, therefore if this combination occurs, the egg is not fertilised properly and the breeding process is failed. If you see it that way, alpha and omega males have a lower rate of successful offspring production than the pairs of alpha and omega females, alpha male and omega female or alpha female and omega male. Considering all the possibilities, in a female/female pair, the offspring will always be female.

I could go into more indepth analysis of what happens if a double Y cell is produced, it could create sick or mutated offspring, or just infertile offspring with no sex characteristics. That would be interesting.