This is an Arizona tax credit program. To be able to take the donation as a dollar-for-dollar tax credit the donor must have an Arizona tax liability and be filing an Arizona tax return. People with no income in Arizona don’t file Arizona taxes and therefore don’t have any liability to take the credit against.
With that said, Arizona Tuition Connection is a 501(c)3 non-profit organization. If people out of state would like to support your family they can make a donation. Instead of being a dollar for dollar tax credit these out of state donations are taken as a federal tax deduction. Donors claim it on their federal tax forms just like they do every other charitable donation they make.
Non-tax credit donations are not limited to the maximums set by the state for tax credit donations.