One way to ask a question in English is to use subject-auxiliary inversion, for example
It should. - statement
Should it? - question
So it is reasonable to expect that the same would apply to questions phrased in the negative:
It should not.
Should it not?
In format written English, this is the correct way to proceed, but in spoken English it is normal to use contractions, and when a negative contraction is used, the subject is moved after the contraction, rather than after the auxiliary verb:
This is true for for all auxiliary verbs - do, would, must, need, have...etc.
"shouldn't it" is perfectly normal in spoken English in the US and in southern UK, though in north-east England and Scotland, you are more likely to hear "should it not".
In written English, contractions were considered wrong: when I sumbitted my thesis, the external examiner refused to accept it until I changed 21 instances of "can't" and "don't" to "cannot" and "do not". They have gained ground over the past few years as written English becomes less formal. Most instances occur in dialogue in novels, like the first two examples below, but it is also used in informal non-fiction books, as in the third example below. There are nearly two thousand occurrences of "shouldn't it" on this site, and very few seem to be in dialogue.
"Yes, I know; God why is life so bloody difficult; love should be easier than this, shouldn't it?" - Ordinary People - Phil Boast
“It should be okay, shouldn't it?" - Winning over Sklya - Julianna Morris
As a concept, joining forces and finances to buy property should certainly make it easier, shouldn't it? - Mortgages made easy - Bruce Brammall
The example that you quoted looks like it is dialogue, even though you may have seen it written down, so I am not at all surprised by the informal usage.