NJ NY W2 Wages

Hi,

I saw some others post here about their NY NJ multiple W2 problem but didn’t exactly see the answer to my questions

I received two W2s for 2019 in separate envelopes. 

Back in Jan 2019, my employer’s payroll department was late in updating my location code from NY to NJ (even though I was working in NJ and not NY from 1/1/2019 and NJ is where I live also for entire 2019)

as a result on payroll of 1/6/2019 I have a small NY withholding

When

First W2 — state NJ - Full Federal income is mentioned against NJ also with NJ withholding X 

Second W2 - state NY - to my surprise here also full Federal income is mentioned against NY and the small withholding amount of the first pay of 2019 as mentioned above

Is this normal ? 
why is NY income shown the full amount? isn’t this double counting ? 

 Ideally I shouldn’t even be filing for NY tax this year had the small NY withholding 

secondly when I put the wages as shown on W2s the program shows me  a huge amount owed to NY and for NJ most of the amount as refund. 

Firstly isn’t this counter intuitive ?
that the state where I  lived and worked for the entire year almost is giving me a refund of most of the withheld tax (Due to credit for other jurisdiction) while the state where for a technicality I worked ( I actually didn’t ) is getting all the taxes! 
Is this how it works for people with NY NJ W2? 

Secondly , isn’t this also causing a  higher tax burden for me as NY taxes are higher than NJ?