For the purpose of ASF (a "limitation") medium mithral armor is considered light
Armor proficiency (Light/Medium/Heavy)
Benefit: When you wear [type] armor, the armor check penalty for that armor applies only to Dexterity- and Strength-based skill checks.
Normal: A character who is wearing armor with which he is not proficient applies its armor check penalty to attack rolls and to all skill checks that involve moving.
Most mithral armors are one category lighter than normal for purposes of movement and other limitations. Heavy armors are treated as medium, and medium armors are treated as light, but light armors are still treated as light. This decrease does not apply to proficiency in wearing the armor. A character wearing mithral full plate must be proficient in wearing heavy armor to avoid adding the armor's check penalty to all his attack rolls and skill checks that involve moving. Spell failure chances for armors and shields made from mithral are decreased by 10%, maximum Dexterity bonuses are increased by 2, and armor check penalties are decreased by 3 (to a minimum of 0).
If you do not have proficiency in Medium armor, then you will take a penalty to attack rolls and all skill checks that involve moving. This would include spell attack rolls. (Since it is mithral, the penalty will be reduced from the usual -4 down to only -1).
But for purposes of movement and other limitations (which includes class features, eg Ranger's combat styles, Summoner's ASF) it counts as Light.