ACT has a tradition of doing intensive, experiential training in addition to training in the core skills and competencies needed to do ACT. Why are these part of the ACT tradition?
These trainings are not training in doing ACT per se -- they are more oriented toward learning what it feels like and how it works to adopt a defused, accepting, present-focused, mindful, values-based posture with regard to your own issues. These experiences are not meant to be therapy. Unlike other traditions, there is no belief that you have to somehow get fully analyzed (etc) and thus no longer be reactive in therapy in order to do good work. The point is not to be the world's most mindful or accepting human. The point is to learn to discriminate these states of mind to a degree that allows you to track what is happening during ACT intervention, and to have some skills in sitting with the painful space of sitting with another human being in pain. We hope that doing some experiential work with yourself will humanize and level ACT work because you learn how hard it is to do the things you are going to try to establish in others through ACT.
There are curently no data showing that these kinds of trainings are needed to learn ACT, and even if you do them, they will not remove the need to learn ACT as a technical matter. This means you should not feel pushed to do them, especially if you are still just learning about ACT and your gut sense is that you might not respond well to such an approach. In that case, do more didactic training first and talk to others about their experiences and then decide.
If you do such trainings remember this: you should never go beyond what you are willing to do. I always tell people to say and do only what they are willing to say and do, and to try to do the work of acceptance, defusion, mindfulness and so on with their own issues within themselves first, and to express that (if they choose) to others as an outward expression of that work, not as a substitute for it. The ACT model itself suggests that blurting out past pains (for example) can itself be traumatizing if it is not associated with acceptance, defusion, and mindfulness.
Having said that, thousands of people have done more experiential training and the very subtitle of the ACT book says that it is an experiential approach. There seems to be something worthwhile in this type of training. Just don't allow yourself to feel forced into anything and don't mistake these experiences as a substitute for training in the technical skills involved in doing this work.