Yeah, you would have to use one of your normal actions to cast those spells. They're extra options, not extra actions. This applies to the priestess and beastmaster abilities. Like other mages, they could cast up to two quick spells in a round, one with the quickcast action and one as part of their standard action phase.
The case with the hydra is different. A creature with the counterstrike ability doesn't have to use one of its normal actions to make the counterstrike, it happens as part of the attacker's attack routine.