The walk behavior (and other physics behaviors) are like this unfortunately. When “on”, the behavior does its thing - when “off” it does not. But on/off, as you note, is not intuitive unfortunately.
If you are recording and have that behavior armed, it is controlled by your keyboard. Otherwise it is controlled by the current scene and playback position - even if paused.
If you can get the job done with the restrictions above, go for it. However the best advice I have seen (I don’t use the walk behavior much myself) is
* Remember that the refresh button puts the character back to its starting position (based on Position X/Y properties)
* If you understand when the keyboard takes effect, you can stop it walking around by enabling recording or disabling that track (unclick the “eyeball” symbol)
But its still painful. So my best suggestion is really
* Turn off the body movement so it just walks in place
* Use the Transform behavior with blends to make the puppet move instead of the built in walk behavior
Doing this you get more control over when the puppet moves or does not move.
This is one behavior that I think Adobe should look at controlling from the timeline so it works out the current body position frame relative to the start of the take. You should be able to compute the position and position of knees, feet, etc based on a time delta from the start of the take. Some of the other physics behaviors this is really hard to do - because objects may bounce off other objects - but I think the walk behavior is deterministic and not dependent on other objects in the scene. Until then, I recommend turning off body movement and using blends of Position X/Y recordings to move the puppet around. Only use the body movement setting if you are doing a live stream.