Tell me if you find anything. Calling a spirit is a simple action for me, not the spirit. And then he appears and ready to go. I didn't find anything in the books or the net, but here's how I imagine it:
Summoning: you take your complex action, which usually costs you a combat turn, and when you are finished, the spirit appears. At the end of the turn, so he doesn't just stand blindly there with mouth open.
Calling: you snap your fingers and the spirit, which was waiting, appears. He's ready to take action with your initiative score (I swear I read this somewhere).
Example: guard goes to the bathroom. Fighting erupts while he is in there. Anderson and Rafa acts, then the guard (with 2 IP) opens the door (takes a surprise test - success) and jumps into the fight. Now he may roll INI, but if he rolls greater then Rafa, can he act before him? No, because he just now joined the fight. Does the guard needs to stand there with his 2 IP-s, watching us running around, with no chance to act before the Mob does, even if he has augmented reactions?
And spirits have 3 IP-s while in astral, meaning they are 3 times faster to react then a person.