Nonresident tuition is two different parts; 1) resident tuition (the base rate of tuition everyone pays) and 2) the nonresident differential (the additional amount that nonresidents pay). When you set up a budget there are individual flags for each section of tuition on M7-16.
If you request that nonresident tuition be paid by your budget then the flag for the nonresident tuition portion will be flagged. But this only applies to the additional amount non-residents pay. To pay all portions of tuition you need to check both non-resident and resident tuition. (See next question)