Can I download Apps on new Apple ID without old ID knowing?

If i have a new apple account and still the old apps from my old apple id, if i download an app from my new account will the person with the old apple id see what i downloaded?

For example, now I have my iPad and my iPhone with my Apple ID but previously my iPhone had my dad's Apple ID. For the apps that were installed I needed his Apple ID password in order to update them. However, now I installed an app on my iPad (on my Apple ID) which I can just download it because it has the cloud arrow symbol on my App Store.

My question is if I download that app on my phone will my dad be able to see that I downloaded it? (The app is currently connected to my Apple ID)

[Re-Titled by Moderator]