Description of the Announcer badge reads
Share a link to a post later visited by 25 unique IP addresses. This badge can be awarded multiple times.
I have just earned the fourth one. And for none of them do I actually remember when and how did I share a link that later resulted in my earning this badge. Is there a way to find out?
Generally, only links from outside the network should count for publicity badges (Announcer, Booster and Publisher). But it seems that there are some technical reasons which might cause that sometimes visits from links within the network count too.
It used to be the case that only links from outside the network contributed to publicity badges (Announcer, Booster and Publisher). Since the switch to HTTPS, the links within the network count too. (But even before that, they might have had some effect for technical reasons.) You can find some more details in some posts on Meta Stack Exchange related to this topic: I received the Announcer badge for a link to a site-meta shared on a hot network question, Publicity badges might be taking internal links into account? or Won Announcer badge even without sharing the link externally.
I think this might be plausible explanation in your case. At the moment you have four Announcer badges. You have linked somewhere on MO to those posts:
You can avoid these badges if you use link without your user id. This discussion is related (to some extent): Privacy of software-generated links to questions and answers. I have mentioned various ways how to link to Stack Exchange post in my answer on Mathematics Meta: Distinguishing between questions and answers in references.
This is only tangential, but since you asked how I found your comment. Initially I tried to google for "https://mathoverflow.net/q/130980/41291". (Just to check whether in this way I can find some places where the post is shared with your user id.) But if you suspect that links are on this site, then you can search for posts containing the given url and restrict the search to a specific user. To search in comments by a specific user, you have to use Data Explorer, here is an example of such query. See also: Searching for comments.
