I do 95% of my indoor training on the Omnium and it’s usually smooth. I do use a trainer specific tire (Conti Hometrainer). My experience with rollers and this trainer is that occasionally I’ll feel a little vibration on the rear tire, mostly it feels like the tire has some extra rubber on it and is bouncing each wheel rotation. I’ve always chocked that up to just that, rubber on the tire as it’s sheds (this happens especially on newish tires as the bead wears off). On older tires I’ve never noticed this.
Vibrations like you described I’ve never felt.
I’d start trouble shooting with your rim/tire. Making sure it’s all true and the tire has no bulging. Then I’d look at the drums on the Omnium. Are they true? Are they too tight? Are they hitting something on rotation?