Yeah, a lot of those people don't get the concept of US citizens living abroad.
I found
this:
Individuals. The purpose of the general definition is to include in the category of individuals who are taxable on their entire net income, regardless of whether derived from sources within or without Illinois, all individuals who are physically present in Illinois enjoying the benefit of its government, except those individuals who are here temporarily, and to exclude from this category, all individuals, who, although domiciled in Illinois, are outside Illinois for other than temporary and transitory purposes, and, hence, do not obtain the benefit of Illinois government. If an individual acquires the status of a resident by virtue of being physically present in Illinois for other than temporary or transitory purposes, he remains a resident even though temporarily absent from Illinois. If, however, he leaves Illinois for other than temporary or transitory purposes, he thereupon ceases to be a resident. If an individual is domiciled in Illinois, he remains a resident unless he is outside Illinois for other than temporary or transitory purposes.
So it seems to be a question of intent. I think honestly if Illinois came after you for your vast sums of money
you can point out that you are here on a settlement visa and intend on residing indefinitely outside the US.