What you see is the method that Delaware uses to calculate Delaware nonresident tax.  Delaware does not tax your Illinois income; however, it does pretend that all of your income is taxable in Delaware, calculates out the tax, and then prorates the result to the percentage of income you earned in Delaware.  Since these calculations all take place on the Delaware nonresident return, it gives the appearance that Delaware is taxing your Illinois income.  But they are not; they are only using the income to determine the tax on your Delaware income.

Given the progressive nature of DE taxes, doesn't the pro-rating approach mean you potentially pay more DE tax than if you simply calculated the tax on the DE-only income?

(I know you didn't write the tax laws, but just trying to understand!)

Perhaps, but the laws can be written an infinite number of ways to get the result that is wanted.

Maybe this will help your situation.

A Delaware part-year resident may elect to file either a resident or non-resident return.  You may wish to prepare both a resident and non-resident return to see if one favors your income and tax situation. 

File only the return which is more advantageous for you.

See page 2 Delaware Form 200-02 NR.

The guidance in the instructions (below) was steering me towards the non-resident form.  (I made a little money while living and working in DE, but made more while living and working in AZ.)  However, I guess I need to look at both and see what works.  Thanks again.

Part-Year Residents electing to file a non-resident return – This
option may be advantageous if, during the period of non-residency,
you had any income from other states or sources outside of
Delaware.