It appears that newly created animation blueprints will fire themselves during any form of PIE if they have been newly created during that session and even if no assets in the scene reference them at all. Restarting the editor alleviates the problem altogether but it’s still a weird bug.
I was able to reproduce this issue following your repro steps and have generated the following bug report: JIRA [UE-9528]. If this issue is addressed, an update will be added to this post.
Are you still experiencing this behavior in the latest version of the Engine? I was not able to reproduce this behavior in UE4.12.5 but I wanted to make sure I’m following the repro steps correctly since it’s been a while.