The issue for state taxes and scholarship income for nonresidents is- whether the scholarship is state source income. In general, a state taxes residents on all income regardless if source and nonresident pay tax on state-source income which includes services performed in the state.
The IRS considers scholarship income unearned unless services (such as teaching, research etc.) are required. If this is the case, then the scholarship would be taxed to nonresident students. (See https://www.mass.gov/directive/directive-95-9)
Most unearned income is not taxable to nonresidents so it would only be reported in the resident state. While it is true that the scholarship is from an Alabama school which could classify it as state source income, other unearned income (think interest or dividends) is not state sourced to the location of the payer.
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