It is somewhat well known that in 1860, South Amboy encompassed a far greater area than in does now, including much of today's East Brunswick, South River, Spotswood, northern sections of Old Bridge and a bit of Monroe Township. But someone more experienced and knowledgeable than me should weigh in here or refer us to a map or some other resource that could better answer this interesting question. I know if you took the time to read up from some of the "History of Middlesex County" and/or "History of New Jersey" reference books written in the past 125 years, some answers lie there.
And yes, even a call to the reference librarians in today's muncipalities or a proper Google search could tell you what year each of these towns incorporated "away from" the original South Amboy. Good luck searching and also with the snow today!