Seems to be a lot of confusion here. Conviction is important to evocation because it determines how powerful a spell you can cast, and how much stress you take just to come up with the necessary power. Remember that YOU choose the power level of your spell; it's not determined by die roll. You take 1 stress for casting at all, then an extra stress for each point by which your spell's strength exceeds your Conviction. So if you cast a standard flame bolt and decide to make it w:5, that's a 5 shift effect. If your Conviction is 4, then that's 2 stress: 1 for casting, and 1 because it's 1 point more than your Conviction.
Having done that, the next step is where you control your spell, which serves two purposes: determining if the spell was properly controlled and determining how well you hit your target. Both are determined by a single roll of your Discipline -- this is where Discipline becomes cruicial. For the control portion of the roll, you are comparing your Discipline roll against the power of the spell (the same number you decided on above). If your roll was at least that, all is well. If it's less, then you are going to take backlash or fallout from your lack of control. Once that's determined, compare the same Discipline roll against your target's defense roll to see if you hit. If you miss, then the stress, backlash, and fallout were for nothing. If you hit, then you figure out damage the same way you would if you swung a sword at your target. That is, you get damage based on how much you exceeded the defense roll, PLUS the weapon strength of the spell, minus any armor the defender has.
So Conviction and Discipline are both very important to spellcasting. If you have a low Conviction, you will be limited to weak spells, or you will tire quickly due to the stress for drawing the power for the spell. If you have a low Discipline, then you will be limited to weak spells, or risk damage to yourself and your surroundings from backlash/fallout of poorly controlled spells, AND you will tend to fail to cast the spells properly, as well.
Harry has a high Conviction and moderate Discipline. He can cast powerful spells fairly well ... but they tend to burn down buildings (fallout).