I don't think it's accurate. It looks like they changed the income tax withholding but not the other state payroll taxes.
There should, of course, not be any CT withholding of any kind. Not CT PFLI or anything else for CT. You are not a CT employee.
They should be withholding NJ UI, SWF, and FLI. UI and SWF are usually combined into one deduction, and it's usually just called SUI or NJSUI. But it's okay if they split it up. I'm pretty sure they should also be withholding for NJ state disability insurance (NJSDI), unless the employer has private disability insurance and is paying the full cost.
Your employer's payroll department may not be familiar with NJ payroll tax requirements. From what you've said before, you might be their first and only NJ employee. They should consult with an expert at their payroll service, if they are using a service, or with some other expert who can advise them on NJ payroll tax requirements.
You should try to get them to reverse the CT PFLI withholding, refund it to you, and make sure it does not show up on your W-2 at the end of the year. I suspect you would have a lot of difficulty getting it refunded by the state at the end of the year. It's a mistaken deduction.
