The solution has been found.
The issue is caused by assigning a button for "TO CONFIG" to your controller. When you push the button of the controller, depending on your setting, it will trigger the LVAR "PUSH_ECAM_TOCONFIG" to 1. In that state, you will get a configuration warning after landing.
To solve this, I programmed my button to trigger "TO CONFIG" switch once on press and once on release. That would set the "PUSH_ECAM_TOCONFIG" to 0 on the second trigger, and you will no longer have a warning after landing.
C. Schaffhausen's post in 1.0.9 - Master caution "Flaps not in T.O. config" after landing was marked as the answer