Noting it is a 2014 model, sadly, it would come as no surprise if the shipping blocks in the springs had not been removed given the number of reported cases on here but that said, your 'incident' makes me wonder if the rear tyres have good tread and are a decent brand?
I found with the 370 that once the tread got down to around 3mm grip starting falling away quite sharply and with a potentially tail-happy car will let go all too easily if the loud pedal is exercised a little too vigorously and noting the speed and you were in third gear at the time.
Also, if the shipping blocks are removed and the tyres are good, if a 4 wheel alignment has not been done that is a must in my book - every year with both my 350s and 370 that was checked and even in those timescales the tracking etc needed adjustments.
Oh, and if the shipping blocks are still in place and the warranty has expired I would be taking if back to the supplying dealer (hopefully not far from you), and banging the table that they failed to do the PDI properly and hopefully negotiate a free service to avoid you raising a formal complaint with Nissan.