Tyres can be bloody aweful, and if they're a step-change in grip from what you're used to it's perfectly possible to spin the car while driving normally and in a manner that would normally be considered safe and within normal limits, but especially if other conditions occur at the same time (wet/poor surface etc) but it's not really an excuse as such. I have recently replaced a set of "doublestar" cheapo tyres with 5mm of tread that were up front on my car (came with the car). When I first got it I fairly regularly would push the nose of the car straight through roundabouts as it simply wouldn't grip as I expect any normal car to do so. Even driving 'sensibly' and often slower than most of the other traffic in the area it would fire its ABS left right and centre, it'd struggle to deal with even light acceleration in the wet and the front end would step out over the slightest of uneven surfaces, even with new shocks. In the first couple of weeks I even had to dodge into a soft verge as braking from 35 on a wet morning they simply gave no braking despite the ABS attempting to un-lock them, it bearly even steered. They were horrific tyres and I dreaded going out in the car even on a good day and even driving like a granny. I planted a set of Uniroyal RainExperts on it (all round) and it has transformed the car, the difference is night and day. the ABS actually works now because the tyres are gripping and it corners well for a FWD nose heavy diesel estate. But I did research the Uniroyals for about 2 weeks and eventually order them in myself as no tyre places locally would get them.
They were mildly slippery for the first couple of hundred miles but afterwards were fine.
Something a lot of people forget is that brand new tyres, even of the same make, will be less precise and grippy than their old tyres as older tyres have more worn tread blocks, though mostly in a the dry. Tread blocks are normally wider at the base and when they are 8mm tall they flex a lot, this can give a predictable slip near the limits, but when they are worn down they dont flex and grip a little more like a slick.
At the end of the day you've changed the thing that connects you to the road, the first thing I do when I do this is take the car to a known quiet safe location at night (car park) and scoot about a bit to see how it grips in comparison with the old tyres, in a place where no-one is likely to get injured. You'll never get your money back on the tyres because you'd have to prove they were not fit for purpose, which they are – your tyres are gripping and you're not sliding off to oblivion, so its personal interpretation as to how that grip is rated.
