To be honest if you watch the first video it's the same corner on both occasions and the same driver. I can't see the car twitch or anything, also weirdly look at the way they drive... What did my track day instructor tell me? Use all of the road 
The editing is playing tricks with you. They probably only had a few external camera shots. I doubt that internal camera shots would be for the same corners or show understeer for that matter.

I had a quick scan through some of the comments. The reviewer commented, "The tires were Bridgestone S0001s, part of the performance package from the factory. They had surprisingly low grip levels and as soon as they squealed at all they gave up."
There were a couple of interesting comments - "he hates the tires ? I hate his slicked back hair and red t-shirt.."

And - "The car CAME WITH THOSE TIRES. So, by definition, IT IS THE CAR...."
I wonder how many people didn't like the GTI, thinking 'IT IS THE CAR!' When it was actually the tyres.
True story - remember the really bad winter a few years ago - I know a woman who change her new Audi A4 for a 4x4, because the A4 was so bad in the winter. So she changed a car with summer tyres for a 4x4 which probably had all-season M+S (Mud and Snow) tyres. I pointed out to her that she should have just changed the tyres. She hadn't thought of that and said it would have been much cheaper.

People think 'IT IS THE CAR'. In reality it is just the tyres. Changing the tyres can make it feel like driving a better car. Or the car just handling the way it should.