The correct answer to your question is what you express in the form of a quotation (presumably from the New Jersey Division of Taxation), near the end of your question.
". . . if you are considered a New Jersey resident for tax purposes, you are
subject to tax on income from all sources (worldwide income), regardless
of where you are living."
That is the way it works in most states, and certainly how it does in New Jersey. As a resident of the state of New Jersey, you are subject to state taxation on all of your worldwide income. Thus, you could work a (temporary) job in Japan, or own a rental property in Poland . . . and New Jersey will tax you on it, as long as you are a New Jersey resident (actually, it's called your "legal domicile" in the colorful language of tax law).
Sometimes, there are mitigation mechanisms in place to eliminate double-taxation, such as if you were to take a particular job in Pennsylvania, for example, you wouldn't have to pay income taxes to both states on your wage income -- but sometimes there is no such relief.
The tax laws may not always seem fair; and we would not disagree with that assessment. However, at the same time, the tax code is simply a set of rules that governs civil society, and occasionally it isn't fair or equitable.
We are sorry if this answer is something other than what you were hoping to hear, but at least now you have the facts. Thank you for asking this important question, and good luck with your rental activities.
