You do not need to have your vaccine records submitted into the app. A lot of individuals are not even able to upload their documents including myself and my wife. We were in Indonesia last month and as US Citizens there was no way to upload our CDC Vaccination Certificate.

You only need to have the app installed along with a created profile. Just bring a hardcopy of your vaccine certificate or have a photo of it on your phone. We always had our physical CDC cards with us but a lot of times all we did was show pictures of the cards and they were fine with that. If they ask for the app just tell them you could not get it to work. They typically don't even care if you're a foreigner because they don't want to be bothered with verifying.

We traveled domestically by train, plane, and visited every type of public establishment whether it was a mall or a restaurant and not once did we have a problem with anyone not accepting our CDC vaccination card.