It is if your new tires are defective.

 

Is there any way to know if the tires are actually defective?

 

You could have a road force balance done on your tires (assuming the shop or another in the area has that machine and knows how to use it) and they can tell you if they are out of spec. But in my opinion it sounds like its an alignment issue not a tire issue. If the tires are out of spec they tend to cause steering wheel wobble like they are not balanced. Even if they are causing a pull moving them around should have altered the way they were pulling. It took my shop a couple of tries after my level kit was installed but they got it right. If this shop is unwilling to keep trying I suggest checking with another one.

 

I forgot to mention it also pulls left when braking. Could all of this be caused by a brake problem?