Maybe it's even more like "I got an outlook message" instead of "I got an email". Since email is an analog of ActivityPub. Just that people are not used yet to the fact that social media can be interoperable like email, so "saw on lemmy" carries different connotations. It should not, however.
Anecdotically, I have an old frendlica account too, from times of diaspora, and it's now very lively, so I saw this post on frendlica too.