A Sahir has a summoning strength of Summoning Total -spritits Might Score.
Is that Might Score also affected by the local aura? I am not sure why it would not be, but it would lead to some counterintuitive results if it did.
For instance, suppose that the Sahir wanted to refine Vis. and he has a choice of two auras to use, one a magical Aura of 3 and the other a Divine Aura of 3. Suppose he has a Solomonic Sihr score of 15, a presence of 2 and without loss of generality, suppose he rolls a 6 on the stress dice of the summoning. Suppose he is summoning a Might 15 Internal Jinn. Assuming that might is not adjusted, the summoning Strength would be 6+2+15+3-15=11 in the magical aura and 6+2+15-9-15=-1 in the Divine Aura. However, if Magical Might is effected by aura, the summoning strength is 6+2+15+3-(15-3)=14 in the Magical aura and 6+2+15-9-(15-15)=16 in the Divine Aura.
Aura shouldn't increase the might score.
Aura modifies the resistance of creatures, based on their native realm, and their current realm. Might is never actually increased in cases where the native realm of the creature matches the current active realm.
As J.L points out, the Might Score of the Jinn is not affected by the Aura.
Ofcourse, the local Aura is added to the Sihr roll, so you would probably generally prefer to summon in a strong, friendly aura.
If Aura was substracted from Might, it means that supernatural creatures could get killed or dissipated by entering strong incompatible Aura. Magical beast and other faerie animal of some mages might not be able to follow their master when they enter Divine or Infernal Aura...
Hi there! No, Summoning Strength isn't affected by the local aura directly, though it does figure into the Summoning Total. Think of the sahir's Summoning Total as the total amount of "magic pull" that he has over the spirit. If it's greater than the amount needed to summon it, the excess pull continues to aid his magic working through the spirit, but it's based on the existing Summoning Total, not a new effect.