Core muscles are used in EVERY Pilates exercise
The core muscles are part of the powerhouse set, therefore engaging your core during Pilates movements is a component of activating your powerhouse. Deep stabilizers such as the pelvic floor, psoas, multifidus, and transverses abdominis, among others, make up the core muscles. The core muscles, on the other hand, are not the huge movers like the rectus abdominis or glutes, which are included in the powerhouse group.
The gluteus maximus is a muscle that helps establish a posterior pelvic tilt and is used in forceful activities that involve hip extension (jumping, stair climbing). This postural component is vital in achieving the neutral pelvic posture employed in Pilates, which is why students are taught to perform a butt squeeze to activate the glutes in the powerhouse in classic Pilates.
And yes, every Pilates exercise, even the stretching ones, uses core muscles. It's either the major emphasis of the exercise, or they're used to supporting you as you move and work other parts of your body.
However, because it is impractical to keep these muscles fully engaged for a whole 1-hour lesson, it is recommended that they be approximately 30% engaged during the class. Some workouts necessitate a little more effort, while others necessitate a little less.