Sign in with Apple

I’m wondering how SIWA works in the following scenario.

I’ve used SIWA for two apps: LG ThinQ and BAND.

After installing both apps for the first time, I chose to Sign in with Apple. Both apps appear under “hide my email“. (photo attached)

Due to some issues, I had to uninstall the apps. I’ve just reinstalled the apps and I want to login using the same SIWA emails/accounts ALREADY created. When I choose SIWA it shows my main Apple ID and not the HideMy random emails.

my question is… If I use as SIWA will it link back to the account already created for the specific app without sharing my main Apple ID?