Usually income is sourced where it was earned. So technically this is AZ sourced income and you should file a non-resident AZ state tax return. Since you will need to file an IL resident state tax return and resident states require you to report all income from sources both inside and outside the state, you will be required to include this AZ sourced income on your IL resident state tax return.
You will get a state
tax credit in IL for the AZ state taxes the your paid on your nonresident AZ
state tax return.
You will want to
work on your non-resident AZ state tax return first. You will then take a tax
credit from your non-resident AZ return on your resident IL state tax return.
(Please note that you will only get a tax credit for your AZ taxes up to the
amount of IL taxes that would have been paid if the income was earned in
IL).
Just follow the
TurboTax guide when working on your states (remembering to do your non-resident
state return first) and TurboTax will do all the calculations for the credit to
your resident states return
Here is additional
information about filing in multiple states
https://ttlc.intuit.com/questions/1900021-when-would-i-have-to-file-returns-in-more-than-one-state
