From the 3rd paragraph. However, yes the alternate universe comes into existence when you reach the singularity.
Still, if you can exist both inside and outside, then your ashes can exist in both places alongside living you without causing a paradox because you simply will not exist in the same space as you ashes that will arrive very much later anyway as time slows at the edge of the black hole. You are more likely, having read the article, to have a post-life crises knowing that outside the black hole you are dead.
The half of your light cone that extends into the future remains entirely within that event horizon. The outside observer's cone can remain outside of it only as long as she avoids crossing the event horizon.
Even if the outside observer decide to jump in just seconds after you, it is possible that the physics inside the event horizon would prevent her from ever catching up with you to compare notes, or even sending you a message. You could send a message with modulated x-rays, and she might pick them up with a VLF antenna. She might reply with a deep infrared laser and accidentally cook your brains with cosmic rays. Assuming a steep spacetime gradient as you approach the singularity, everything sent inward would be severely blueshifted, and everything sent outward severely redshifted.
There might even be a sort of Zeno's Paradox inside, where once you cross the event horizon, there's another event horizon beyond that, such that anything that much closer to the singularity than you are can never communicate with you, in the same way that you can never communicate with the universe outside the first event horizon.
Isn't every step in from the event horizon effectively an event horizon? If all the mass of a black hole is effectively at the singularity in the center, and escape velocity is the speed of light at the event horizon, won't there be no point within the event horizon where escape velocity is less than the speed of light, such that at any point within the event horizon, no point farther from the event horizon is within the future light cone of that point.
Ah, I'd assumed this meant that "you" would split in two, both copies being "in the same universe". I don't know enough about the physics to know which is meant.