It's easy to miss, but it says on p. 251 (just before the example) that the Discipline roll used to cast the evocation counts as the attack roll. The amount of stress inflicted by a successful attack is equal to
(attack roll - defense roll) + weapon rating. In the example, the relevant numbers are:
- Attack roll: 8
- Defense roll: 4
- Weapon rating: 8
attack 8 - defense 4 for success and stress of
4. Since this attack was made with a weapon, now add the weapon's rating:
stress 4 + weapon 8 for a total of 12 (less one for Inhuman Toughness).
The math isn't the same at all in the case of losing the opposed roll. If the attack roll doesn't beat the defense roll, then the weapon rating is never factored in and the equivalence breaks down.
So it's not quite "shifts you put in plus your Discipline roll" minus defense, it's the mathematically-equivalent (but procedurally and conceptually different) "attack effect plus weapon rating". If it's easier to remember the first way then that's fine, if you win the opposed attack/defense roll. If you don't win the contest, then thinking of it as "shifts plus Discipline" will just cause confusion.
Here's an example of how the math works when the attack loses the contest:
Harry is fighting one of the Vampire's minions now. He fires off the same evocation that took out the minion's master, putting in 4 shifts—he doesn't want to deal with backlash or fallout just to deal with some poor thrall.
Harry's evocation is a weapon:4 and his Discipline is Great (+4) so he only needs to roll 0 or better on the dice. He rolls 1, so his total Discipline roll is 5. That's enough to control the evocation, and doubles as his attack roll against the minion.
Against all likelihood the minion rolls exceptionally well, getting a +6! Harry's loses the opposed roll and his attack fails, even though he cast the spell successfully.
Now, the numbers look like this:
Discipline roll: 5
Shifts put into the spell: 4
Attack roll: 5
Defense roll: 6
Weapon rating: 4
If we use your math, then the attack is
Discipline roll + shifts in spell:
5 + 4 for an attack of 9. Less defense of 6, that would deal 3 stress to the minion.
However, that's not how attacks are resolved! Using the actual math, the attack is
(attack roll - defense roll):
5 - 6 which is -1, and since rolls never generate negative shifts (p. 17), the attack is just considered to have failed. The minion won the opposed roll and the weapon rating becomes irrelevant—weapon rating is only added to the shifts generated by a successful attack. The minion suffers no stress, and now Harry is in a bit of trouble…