Here is how I did it.
I created a character, put it in a bone layer, and rigged it as follows, a root bone for the main body and four children for the tentacles.

Here's the bone strengths (root bone gets zero bone strength).

I bound the points of the main body to the root bone.

I put bone dynamics on the child bones.
After resetting all bones, I only have to move the root bone, and the tentacles lag behind. When the main body stops moving, I remove the bone dynamics from the child bones, so they return to the default position.

Here is the resulting animation:

And here is the ASP 5.6 file: I hope this will help you understand how to set up secondary actions with bone dynamics.