I’m a PA resident but work in nNJ

Hi so I recently started working in NJ, but am a resident in PA. I had been informed about the reciprocal agreement between the two states (NJ-165) form. From what I understood is that I am exempt from paying taxes in NJ and only pay income tax in PA. 

today I had looked in my paycheck and saw that my social security and federal taxes went up ALOT like mind boggling a lot . But . 
My main question is , why am I paying more ? And because I depend on my pay check so much would you recommend filling out a new W-4 form? If this is the case if I made it to where I got almost nothing back at the end of the year would it be beneficial? 


also when I saw this I contacted  my HR and tried having it reversed to how it was before signing the NJ-165 for…but they told me I can’t  because I have to pay taxes to the state I live in as well.. number one … I don’t think they can deny a reversal on this ! Number two … what difference does it truly make ? If it wasent for me finding this form and submitting it to HR then they never would have been a change or reached out about it at all.. plus to top it off and Plese correct me if I’m wrong . But let’s say I didn’t sign this form . Could I just file for a non resident refund from NJ and simply pay PA back the money I got refunded from NJ with? Because if that’s the case I’ll make sure it gets switched back. 

tge reason why I’m so stressed about this is because when I filed my taxes the other day .. the guy said I don’t owe anything to the state of PA. 

i was expecting too scince throughout the year of 2021 NJ was withholding my taxes . And it wasn’t untill 2022 the PA withholding went into effect on my pay check . Which means I didn’t pay a dime to my state.. so either he did my taxes wrong or there is something that I’m completely confused about and if he didn’t file them wrong then I see no point with this form and then only ask if it’s legal for me to reverse the form I signed