The interest due is a time value of money that contains no qualification that it be calculated from the date that an invoice is received. It is based upon the harm to the sewage company from not receiving timely payment and not on the fault of the customer who doesn't pay on time. This isn't terribly exceptional.
The linked statute states:
(a) In the event that a service charge of any sewerage authority with
regard to any parcel of real property shall not be paid as and when
due, interest shall accrue and be due to the sewerage authority on
the unpaid balance at the rate of 1 ½ percent per month until such
service charge, and the interest thereon, shall be fully paid to the
sewerage authority. . . .
(f) In the event that any service charge of a sewerage authority shall
not be paid as and when due, the unpaid balance thereof and all
interest accrued thereon, together with attorney's fees and costs, may
be recovered by the sewerage authority in a civil action, and any lien
on real property for such service charge and interest accrued thereon
may be foreclosed or otherwise enforced by the sewerage authority by
action or suit in equity as for the foreclosure of a mortgage on such
real property.
Another statute related to this issue is the statute that authorizes the sewage company to charge its customers, the first subsection of which says:
(a) Every sewerage authority is hereby authorized to charge and
collect rents, rates, fees or other charges (in this act sometimes
referred to as “service charges”) for direct or indirect connection
with, or the use or services of, the sewerage system. Such service
charges may be charged to and collected from any person contracting
for such connection or use or services or from the owner or occupant,
or both of them, of any real property which directly or indirectly is
or has been connected with the system or from or on which originates
or has originated sewage or other wastes which directly or indirectly
have entered or may enter the sewerage system, and the owner of any
such real property shall be liable for and shall pay such service
charges to the sewerage authority at the time when and the place where
such service charges are due and payable.
N.J. Stat. Ann. § 40:14A-8.
The interest applies when the payment is not made "when due." This interpretation is supported by a trial court case interpreting the statute and a related contract with the sewage company:
The Service Contract, however, provides that the payments are “due” on
the specified dates, and if payments are not made by those “due
dates,” interest will be assessed from the very first day the payment
is late and not from 30 days thereafter, irrespective of the fact that
the interest may not be collected until after that 30 day period.
N.W. Bergen Cnty. Utilities Auth. v. Borough of Midland Park, 604 A.2d 229, 237 (N.J. Super. L. Div. 1992)
There is no reason to need to say so expressly in the statute because the default rule of contract law is that you have strict liability for meeting your contractual obligations that applies whether or not you are reminded of them with an invoice, and owe interest when it doesn't happen, no matter why it doesn't happen. Unless the contract says that payment is due X days from receiving an invoice, payment is due when it is due whether or not you receive notice of that fact.
Also, the due date is set by the sewer company's board.
In the context of the relationship you have with the municipal sewer authority, part of why that makes sense is that by having a sewer, you know that you will be receiving sewer bills according to a regular schedule, and the onus is placed on you to figure out what is going on if you don't get one.