1st -- I think that this could have been handled by the Simple Q&A thread
(I'm just saying
)
the only way that it would get only 9 rounds worth of actions (to use your example), would be if the casting time counted against its actions -- this is not the case.
There's nothing in between steps 2 & 3 ... it showing up
just before the start of your turn is what allows it to act
on your initiative ... it gets to act for 10 rounds (again, using your example) after it shows up (i.e., after the completion of the casting)
as a side note .... while it is not spelled out,
I would say that they arrive flat-footed until they act. for example, if an enemy realized that you were summoning a creature, and readied an action to attack for when that creature arrived, I believe that that attack would catch the summoned creature flat-footed (but that is purely my own conjecture ... I don't know if the idea has ever been discussed)