Can other people see when I mention someone on twitter (@example)?

[this person]

Okay, so my twitter is public. I want to write someone so I thought I could send a DM (direct message) to them, but I just found out that they have to be following you for you to send it, so I decided to send a regular mention (@example) to them, but I was wondering if I did that, will it show up on other people's homepage? I can see when my friends write mentions to each other, but I have them as a follower/following. For instance I'm friends with A and B, and A mentions B, and B writes back to A. I can see both mentions, but I just realized that one of my friends was mentioning someone that I didn't have as a follower/following. For example I have friend C as a follower, but not friend D. C writes to D, but I don't see what they write until I actually go on their page. I don't remember seeing those mentions on my homepage, so I'm thinking you can only see them when you have that person as a follower/following, maybe? Not sure.