Which is ironic seeing how he is an Uzumaki. So why did Kushina survive that little bit and Naruto just died instantly? That within itself is inconsistent. We also have the Gedo Mazo ripping the Nine-tails out of Naruto and Eight-Tails out of Bee within seconds or minutes when it took 3 days to rip the One tail out of Gaara along with the help of the Akatsuki which is also inconsistent.
There are so many more inconsistencies that many of us have forgotten.
Why is that inconsistent ? First off Naruto is only half Uzumaki , then it doesn't say that all Uzumakis made good bijuu hosts . In Kushina' s case she had the special chakra for that , the chakra chains that allowed her to restrain a bijuu temporarily even without a seal in place and she was brought to the leaf specifically for the purpose of becoming a bijuu host . I think it's safe to say that only a select few Uzumaki's had that ability and most likely only the women of the clan seeing as Mito was also a jinchuuriki and now Karin also awakened the same power , while Naruto never showed any signs of having it .
There's also the seals used for each , which again were different . In Naruto's case the seal allowed the bijuu chakra to seep through . We can not be sure as it is not mentioned but I think for Kushina the bijuu chakra could not flow through the seal and try to control her
So even though both of them are Uzumaki , which is about the only thing they have in common in this , Naruto and Kushina are two completely different Jinchuuriki so it makes sense to me that their reaction to having had the bijuu removed be different .