The book is most likely wrong. Problem with Catalyst is they time-crunch on their books too much and, on this iteration, missed a lot of example things like that. This isn't the only example of a mistake in the book, so don't worry too much.
When summoning a spirit (or sprite, since the summoning and compiling rules are almost identical), you go by the steps in the book (no book handy, but I have this stuff memorized).
Now, since normal summoning doesn't matter too much for this, a mage doesn't usually see this in the rules. However, when you are rolling ANY opposed test, the defender is NEVER limited. Defense pools get all successes that come up, no matter what. This goes for guns, talking, magic, anything. Defense is NEVER limited. Only offence.
Step 1: Choose the Type of Spirit/Sprite
Step 2: Choose the Force of the Spirit/Sprite (Stun Max = Magic/Resonance Rating, Physical Max = Magic/Resonance Rating * 2). This becomes the limit of the test, as all spell casting and technomancer stuff is dealt with the same way.
Step 3: Roll Magic + Summoning or Resonance + Compiling vs. The spirit/sprite rolling their force.
Step 4: Limit your results UNLESS you spent edge during the roll (or if you spent reagents when casting as a mage).
Step 5: Compare your results to the spirit/sprite's results.
Step 6: Calculate drain/fading based on spirit/sprite's force. How this is done is you first take the force of the spirit/sprite you compiled. Is it more then your magic? If yes, you're calculating for Physical. If not, it's calculating for Stun. Next, add up all the gross hits the spirit/sprite made and times by two. That is the amount of damage you'll be needing to drain/fade away.
Step 7: Enjoy your new spirit/sprite.
Take anything from summoning a spirit and it's the same thing you're doing. Again, the only difference is that the mage is able to use reagents to try and kick up his limit (to get a limit of 13, a mage would spent 13 units of reagents). That does NOT alter his magic, mind you. Even if he's only casting a Force 6 Lightning Bolt, if he uses 10 reagents on the spell and gets 7 successes, he calculates his FINAL net hits (7) and compares that to his magic (6). He's over, so that means he's taking physical damage. Now, a mage is able to limit his own successes, if he wishes, to dial down a spell in case this happens. This can happen, usually, with edge. Mage wants to only throw a Force 4 lighting bolt, edges it, gets 12 successes, and is now looking down the barrel of 16+ Physical drain. He can opt to NOT take as many successes so it's just under his force, if he wishes.