The Woman in Black is Arthur Kipps's story. He makes this clear at the end of the first chapter of the book, when he commits to telling the story:
I decided at once that it should be, at least during my lifetime, a story for my eyes only. I was the one who had been haunted and who had suffered—not the only one, no, but surely, I thought, the only one left alive… (1.65)
The entire story is told from Arthur's point of view, which makes us experience all the confusion, realization, and terror at the same time as he does. We aren't privy to the larger picture, just as Arthur is not privy to it until it is far too late. Even though he's telling the story from the present, we almost get to experience the mystery and horror of the journey ourselves.
There is some hindsight involved. Arthur is older and wiser now, which means that he can see the whole arc of the story. And in that story—a story that the woman in black seems to be controlling, even in Arthur is the one telling it—Stella and Joseph had to die.