I want to say right up front that today I'm talking about my teaching style, not other teacher's styles. There are many styles out there that work for different teachers and that work for different students. This is just my story.
The teacher training I took taught us in a participatory role. What I mean by that is that we were taught to teach but also to do the Yoga while we were teaching. To demonstrate the poses. Sure, we would come out of some poses to adjust students, but overall we were doing the asanas with them.
I have taken many Yoga classes of both styles: those where the teacher participates and those where they just instruct. The latter has varied to the instructor giving a short demonstration to no demonstration with just verbal cues on the pose.
As a Hatha teacher, I have always participated in my classes. My head is often up to ensure that everyone is finding their way, providing modifications as needed and checking in on student's progress. However, I've always practiced along with my students.
I recently started teaching Yin Yoga. My initial intent was not to participate in the class, but rather to demonstrate the pose and then guide my students into it. I would spend the time they are in the pose ensuring they were each getting what they needed.
I think in a large group class setting, that would be a great idea. However, since I teach very small group and individuals, I was at a loss what to do with my extra time. I know that it's fine to just sit and watch my students practice. But that's just not me. So, again I find myself participating in the pose once I've ensured my student's needs are met.
It will be interesting to see how this changes and evolves along with my teaching.