Literary Treks had an interesting theory:
Robert April is from an alternate universe.
There are no Prime-universe elements in Countdown to Darkness. See this interview, in particular this quote: "Our instinct now is to leave well enough alone and let this timeline stand on its own." And cowriter Mike Johnson said, "No Prime connections in this one. The priority is exploring this new reality." That doesn't exclude an entirely different universe, but that would go against the grain of their interview. In other words, this is the Robert April of JJ-Trek we're seeing in Countdown to Darkness.