User activity not showing in the personal log but is in the public log using Heartbeat module
Finally sussed it. I needed to go into the Triggered Rules page and change the "do" behaviour for the "Heartbeat: When a user adds a comment" rule.

Setting "User Id" to "[comment_author:uid]" links the activity log to the author, and "Node context Id" to "[node:nid]" links to the node being commented on. After changing these the activity showed up in both personal and public Heartbeat activity streams.

Hope this helps somebody else who may be struggling with this.