Kour, you're confusing the "time" of CT and IP.
One Combat Turn is 3 seconds. Always.*
Then you just look at how many IP's the people in the combat have. In this case, the highest number is 3, so every IP takes 1 second.
A person with only 1 IP can take one complex action or two simple actions + a free action. The first chance he gets to take that action is when his initiative number comes up, but he can choose to delay one or more actions and use them in the later IP's. (Though he must have used them by the time the last IP has passed, he can't delay them into a 4th Initiative Pass)
A person with 3 IP's can take 1 complex (or 2 simple) action every pass. If he chooses to delay and takes actions into a Pass, his others from that IP are lost. This way, he can't hold his actions from IP 1&2 and do 3 complex actions in the 3rd IP. (And same as before, he must take them up before the end of IP3, he can't force a 4th IP to be created)
Things get a bit weird when inserting new combatants/spirits or taking initiative-changing actions (read: Increased Reflexes spell) halfway in combat. The general rule seems to be that new persons should be considered to act like they already were in the initiative, they just didn't know it. So if guard-with-3-IPs opens the door and steps into combat on the second IP, he can still act once in IP3; he does not get 3 passes because "he hasn't had any actions yet".
Things that add initiative or passes usualy only come in play during the next CT (NOT IP). So a 1-IP-mage that gets 2 extra IP's from a spell, gets those extra actions only in the next combat turn, not this one.
Things forcing a loss of actions however, get activated immediately. If a increased-reflexes-pumped-mage gets dispelled in the first IP, he doesn't get actions in IP2. If a spirit loses actions because of materializing (and drops from 3 to 2 passes), he doesn't get to act in IP3.
(* Well, for normal combat anyhow, chase combat with vehicles is different but not important now.)
The only question which remains is if a spirit being pulled out of standby uses an action to show up. Personally, I don't think this is so and I think Eddy could have called the Professor in IP1; the Professor could have then used his IP1 action to materialize and could cast a spell in IP2.
If Eddy had called the prof in the second pass however, the spirit couldn't have done all this in time.
But it's not too far-fetched to assume that a spirit takes at least some time & effort to transfer from its metaplane to this one, so it's your call.
Edit: Ick, Ninja'd 4 times while writing this, no time to catch up now.