the car to feel strange. I've found too high a pressure in the front tires can cause a mild vibration though this is only present -- my experience anyhow -- at highway speeds. Around town not so much.
As others have suggested flat spotting is a possible explanation and I have felt this in my car though this should go away in short order once the car is under way.
As an aside there seems to be a sweet spot in terms of climatic conditions that bring out the worst in tires in this regard. Too hot and the tires do not cool down enough to take a set. Too cold and the tires do not get hot enough that they can develop a flat spot when they cool down. The temperature has to be mild so the tires get nice and hot then it has to cool down enough that the tires take a set.
Anyhow, if the feeling persists longer than a mile or so I'm thinking flat spotting isn't the reason.
Long shot but a tire carcass can suffer some belt or cord or other internal failure. In this case the tire is bad and should be replaced. If the other side is worn more than 30% it should be replaced too. An inspection and rebalance ( using a load force machine ) should find this condition.
Yet another explanation is one or more tires have gone out of balance. What happens is as the tire wears the tread wears away. The tread can have heavy and light areas. As the heavy areas in the tread wear away then the tire which was balanced goes out of balance. The techs tell me this is quite common with Cayenne tires -- they are so large -- but can happen to smaller tires too. Happened to my Boxster once -- its front tires -- and they're 17". The dealer rebalanced the tires at no cost. Might mention once out of a considerable number of tires (268K miles so the car has had a good number of tires on it over the years).
And there is just the possibility a wheel lost a balance weight. The sticky didn't hold the weight, the wheel wasn't clean enough, or when washing the car the jet of water was too strong, etc.
But regardless the shop, the tech, should be aware of all of the above and even more. There's a chance the lug bolts are not torqued properly, the wheel has suffered some structural failure, or the alignment is off or a suspension or steering component has worn out or failed.