Pilates is known for it's focus on abdominal engagement. It is often explicitly cued during classes. The general challenge with this approach is that suggesting to people to "find your tummy", to bring "bellybutton to spine", or to "engage your abdominals" - which you might hear - is not terribly specific and will mean different things to different people.
Here, I would like to highlight what we are definitely NOT wanting to achieve during Pilates classes - and that is "core bracing".
Imagine you have someone coming towards you wanting to punch you in the gut. You will automatically tighten your abdominals if you are unable to avoid impact. The tightening of all muscles around your belly will create a stronger protective corset to protect your middle, and everything will tense. This is core bracing.
The problem with that is if you use this all the time as a movement strategy, the superficial muscles will be overworked and the deeper ones will not necessarily switch on.
That is not how we work with abdominals in Pilates. Instead I use a variety of techniques to connect in a more subtle way. With the breath out, we work to create deeper tension in the abdominals which with time should become an automatic response that you don't need to think about.