What Eric said (quoted). I usually start in March. You can check water temp if you want, or if you just start in March you'll have a good bloom going before the FA gets cranked up.
You probably wouldn't want to fertilize at the same time you apply Cutrine; the FA is going to take up oxygen as it dies, as you've obviously already gleaned. Plankton produces oxygen, but it also consumes it during nighttime when there's no sunlight, so there would probably be an increased strain on the DO levels at night if you had FA dying off on top of a big plankton bloom that takes up oxygen at night. Also, you may get somewhat of a bloom just from the nutrients released when the FA dies, in which case you would need less fertilizer once you fertilize. I would say apply the Cutrine, then wait a week or two and fertilize. And remember - once you get the bloom going it gets much, much easier, and your fish get much, much bigger.
