Ok I'm wrong - people will only see it on their timeline if they follow both me AND the person I am replying to. Had no idea! Better to tweet something myself, and then quote tweet that as a reply if there is something relevant. Learning every day.
BTW - just to clarify something here:
If I reply to someone and my tweet begins by mentioning them - that is when the above is true. Meaning, it's a "true reply" and my followers won't see my tweet unless they also follow the person I am mentioning. However, as in the case of Old Town Road, I replied to lilnasx but I removed his mention. By removing it (or placing it later in the tweet), it is something that all my followers see (even if they don't follow him). This is also why people who reply to someone and want all their followers to see the reply will sometimes put a period in front of the tweet. So it will look like: ".@lilnasx" to start the tweet. In case you were wondering (like I was!) why people do that.
I think it's a solid system by twitter, because I would like to reply to lots of different people without all my followers seeing it every single time, so this gives you that kind of control. Anyway, carry on. #themoreyouknow