Honestly while everyone is like "why did the tentacles not protect Miko" and "oh the axe ghost might not be a bad spirit" the real reason is just that the axe ghost doesn't hit people, he swings his axe and if you're possessed he hits the ghost inside of you drags it out and kills it.
You as a living person go completely unharmed in the process, Miko was scared yeah because she can see ghost and interact with them in ways most people can't so she couldn't be sure that she'd be fine, but she was. So the tentacle entity itself wouldn't react because it knows Miko will go unharmed by the axe ghost.