Appliances are designed to apply pressure correctly.

I experience something like this as I have asymmetries, and the right side of my palate is lower down than the left side. I also am aware that my head tilts slightly to the right. I find that if I consciously tilt my head a little bit more to the left, my left ear towards my left shoulder, and then swallow, the left side of my tongue becomes more active. That is, I can feel it pushing with more force upwards into the palate. You will find that different muscles activate when swallowing with the head tilted in various directions.

I have been doing neck stretches to try and fix this head tilt that I have. I think it is important that we approach mewing from a holistic standpoint, understanding that everything is connected in our bodies through a network of myofascial tissue. This is why focusing on our overall posture is important, practicing the McKenzie chin tuck, and the abs walk that Dr. Mew describes. I haven’t really figured out what the abs walk is yet to be honest.

Anyhow, this is what I have experienced so far. Not sure if that helps you in any way. It is possible that your tongue is simply evening out your own asymmetries.