Yes that is a classic symptom. Especially if pushing in one area of the cone makes it worse, and/or pushing elsewhere makes it better or disappear. The voice coil is wrapped on a short cylindrical piece like toilet paper roll, and it sits in a narrow gap between the outer magnet and inner pole piece. If it's off center it will rub, sound bad and eventually wear through the voice coil wire. This driver may have a narrow VC gap, or it may just be a bad refoam job. I have never shimmed when doing a refoam but it sounds like maybe you should on this one. Actually I had one this spring that started rubbing at high volume, so I may have to get into shimming myself. It's a PITA but it's also a guarantee.