Unlike humnas, no mood lighting is required for crix to breed. It's nearly an impossibility to stop them from doing so.
However, the eggs probably won't hatch before you feed off all of the adults, so keep the tote for a while after the adults are gone to make sure.
Also, if your beardie doesn't eat much, be aware that adult crix are cannibals - You'll want to get the little ones out of the general population.
Frank