Therin of Andor wrote:
a few details about the Prime Captain Robert April
How would the characters know about or mention the prime universe's characters? Beyond Spock Prime?
The JJ Universe's April features in IDW's "Countdown into Darkness" comic mini-series.
You gave the answer: Spock Prime or at least information he gave. Another possibility would be a Starfleet vessel crossing over from the Prime universe/reality similar to how the USS Defiant seen in "The Tholian Web" crossed over to the Mirror Universe.