Can another person see if I accidentally restored from their iPhone backup?

I used to jailbreak iDevices and I had a bunch of other people's iPhone backups stored on my computer/iCloud. I was updating and restoring a personal iPod Touch 4th gen and I accidentally restored from another person's iPhone backup. The screen on my iPod is badly cracked so I couldn't see the name of the backup I had chosen to restore from. (both my name and the other person's name start with the same couple letters, that's all I could see) I went ahead and signed in with my Apple ID on my iPod.

An hour later my mom calls me and said a message came up on her iPhone saying something along the lines of "iMessage on (persons name)'s iPhone is signed in with (my Apple ID)". My mom uses my Apple ID on her iPhone so I'm assuming that's why that message came up. But I immediately did a full data erase and reset on the iPod and set it up as a new iPod.

So my question is, if my mom got that notification, could the other person have gotten that message too? Or does it only apply to the devices signed in with my Apple ID. The other person has their own Apple ID, and I believe they now have an Android phone as well. But I just don't want them to see that message and think I was getting into their stuff and have problems. Although I doubt they even know my Apple ID or even remember I jailbroke their device as this was over 2 years ago, but it still worries me.

Well, the email linked with the apple account will get the message.

Mum needs to get a separate Apple ID.