M. ibericus queens produce ibericus males and ibericus females, so that these can mate and produce more ibericus queens. This keeps the normal sexual reproduction of the species going on.
M. ibericus queens produce ibericus×structor hybrids as infertile female worker ants.
M. ibericus queens produce structor males, so future queens can keep producing the hybrid worker ants.
My guess is, maybe there is some benefit having the workers to be hybrids and not pure ibericus ("hybrid vigor" [1]). So it's worth the effort of keeping the structor males along, to be able to produce the hybrid workers. But I think the pure ibericus genes in the line of queens are in control.