Not living in New Jersey but employed there, I am required as are all CAL employees to pay SDI tax, SUI tax, and NJ Workforce. I have never filed a state income tax form for NJ as I live in a state with no income tax. All I know is that they deduct it.
You may consider consulting a tax preparer, or even asking your employee relations, payroll staff at your airline. It can be a convoluted subject which somewhat depends on whether your employer holds a tax id in your state of residence. And, the laws in the state in which you are a resident, domiciled, and headquartered.
I've had employers which have withheld in my state of resident. Also, I've had employers that have withheld in my state of employment (which I always got back by filing a claim for money earned in another state).
My point is that you may want to talk to someone that actually may know the specifics for your company.
I am based in CA and live in WA. I pay the CASDI. I have heard that at least one of our non-CA pilots did get money from it.
Years ago a pilot (AAL I believe) sued the state of CA for state taxes. The ruling was if you are based there but live outside of the state of CA they cannot tax you if more than 50% of your flying is outside the state.
This tax subject gets very tricky. The reason most employers tax where you are based is 1) they can not get in trouble for not taxing you 2) they then do not have to file tax returns in multiple states every month/ quarter/ yearly.
Technically the company is responsible to pay tax in the state in which the "labor" occurs. Most every state then has an exception if you live in a bordering state to pay to the state of residence. The next issue is that most of us can be considered to be interstate employees. Therefore we fall under the Federal Railway Labor Act of 1984 (could be wrong on the year) and therefore have the option of paying state tax to our place of residence. You must pass the test of being an interstate employee then before trying to flight this one. I do not remember all the requirements but if you do nothing but day and 2 day trips you will not qualify as an interstate employee as you are "not spending enough time away from your home base/ place of employment".
With all this being said it is purely voluntary for an employer to withhold and pay taxes in any other state than the state of domicile.
There is a grand exception to all of this. The state of OH several years ago decide that it was better than the federal government and built laws to suppressed the Railway Act and has this very stupid test with respect to days away/ vs. in OH. It is nearly impossible to qualify to pay other than OH.
I owned a payroll company for many years and several of my clients were traveling construction personnel. The previous payroll companies just taxed everything in the state in which the corporate office was located. I informed them this was incorrect and had to show them how it is really done. OH, PA, NY, NJ, and CA are some of the hardest states to work with regarding these issues.
To get the specifics I would look under the railway labor act though for proof that you could be taxed in your state of residence.