I've had two Dunlop tires that were defective from the get go. Did not cause anything like this wobble but I could definitely feel that something was wrong. I would suspect a bad tire since the problem happened just after the install.
I agree, a brand new tire can be "bad", I'm on my 4th set of front/rear tires and I've had the first and third rear tire and the 4th front tire that were "defunct" (service managers term) brand new .
The first hint was 3 ounces of weights, the second was an uneasy "wandering" feeling.
Manually spinning the rim/tire on a balancer showed that tires "balanced", but weren't "round" and would wobble side to side.
I've never had any issues with any other tires, just these "CVO" Dunlop tires.