If you fertilize now while you still have the algae, which I recommend because it saves a step and unnecessary expense, the algae will very briefly - with the emphasis on very - possibly grow more, perhaps a couple days. But within a week or less, as the plankton bloom occurs, the sunlight will be cut off to the algae and it will die.
All of this is based on a pond that only has algae growing around the edges of the pond - that's yours, correct? If you had FA covering a large percentage of the pond, 40-50% or more, it would be safer to kill the FA first with Cutrine or the like; but if it's only growing around the edges you'll be fine, and you'll save money and time (and labor).
Be sure not to apply the fertilizer directly to the algae - instead disperse it as evenly as possible throughout the pond in three to six feet of water or so. A little deeper is okay; shallower and it could help the FA too much.
If the majority of the pond was covered in FA, its die-off could potentially take up enough oxygen to kill fish. But if it's only around the edges, you'll be fine. I had expansive weedbeds die off two months ago when I fertilized a five-acre pond in which the FA had already gotten a very good foothold, and there was no problem. No matter how you kill the FA, it's going to take up oxygen as it dies; even if you used Cutrine you would still have to be careful if a majority of the pond was covered with FA; the general recommendation in that circumstance is to treat part of the pond at a time. But that's only when a majority of the pond is covered.
The best gauge of how often to fertilize is to use a Secchi disk - there are threads on here telling you how to make one. It's basically a bright-white and black disk that you lower into the water, and if you can see it more than eighteen inches down, you need to fertilize. Usually that's going to amount to once a month or so from March until October, possibly April to September where you live.
