This is wrong information. FLI/SDI/SUI are not part of the reciprocal agreement. The reciprocal agreement only applies to state income tax.
It is not clear what to do when an employer wrongly withholds this tax. Based on this NJ Division of Taxation link, your best bet would be to get your employer to request the reimbursement. I would do the same for paying the correct PA SUI tax that was supposed to have been withheld.
