need help with a backup issue

My iCloud account, and appleID are both completely separate from my mom's accounts. My mom is going to get a new iPhone soon, and isn't that tech savvy, so I backed up her phone on my iTunes on my computer. Before doing that, I logged myself out of iTunes, and logged her in. Then, I did a backup. (although at the top of iTunes, it said it was syncing) But, I made sure I chose backup, and not sync. Everything worked fine- we each have our own content on our phones. But, I noticed today that my app store icon shows a 5 on it. I checked, and all my apps are up to date, but those 5 apps are ones that my mom needs to update on her phone. When I tap on one of those apps, the popup appears that says I need to sign into iTunes with the password for my mom's Apple ID.

Do you think I did something wrong with the backup? She has a 4s, and I have a 6s. I haven't noticed any other issues other than this.

thanks!