There is a muscle going around the mouth like a�racing track�, or a ribbon.
When you firm up your corners you do firm up that ribbon muscle, because that is the muscle you can firm up in the corners. The rest of the ribbon will firm up more or less.
That is not a bad thing. It prevents the pressure from the contact with the mouthpiece from pressing on the teeth. It might close you lips so that you have a problem with your tone production. That can be compensated with the muscles pulling the lover lip down, you heard about the �pointed chin�? That is it. The lips should be �just touching� not pressed together.
Many students play with a very lose embouchure, with a poor range and a kind of soft spread flabby sound. To firm up the corners usually help, many students don�t even notice the tension in the fleshy part because the pointed chin is automatic to them.
However, it is possible for me to tense the fleshy part so that the sound gets funny, the ribbon muscle can be firmed in different ways, let the sound guide you. Long tones. Arpeggios.
Since there are not really any muscles in the parts of the lips that just touch, it is possible to have the ribbon muscle firm and play. Be sure that the airflow does pass through the lips.