I had this issue because I was overapplying. I wanted full colour, so I kept layering, and the excess had nowhere to go except my teeth and cups. Now I use liner first, one lipstick layer, blot, and lightly set the edges. It still looks bold but behaves much better.

Creamy lipstick moves more when there is too much product near the inner lip. I apply lipstick, blot with tissue, then apply a second thin layer only on the outer part of my lips. I avoid putting heavy lipstick right where the lips meet the teeth. Lip liner also helps keep the shape in place.

After applying lipstick, I do the old finger trick. Put a clean finger in your mouth, close your lips around it, and pull it out. The lipstick that would have ended up on your teeth comes off on your finger instead. It sounds funny, but it works every time with reds and berries.