I thought the reason he arrived after Nero was because Nero entered the Black hole first and each were deposited at different places in the timeline.
Yes, but if Nero arrived in the prime universe, a quarter century later Spock should have as well.
He did not travel as far back in time as Nero, he wasn't present when the time lines branched. How did he get from the prime into the alternate? The alternate had sailing away for twenty plus years when Spock stopped time traveling.
Spock needs to figure out how he got from the prime into the alternate. Then (if possible) reverse that event.
The movies TPTB have stated that the prime continued after the split, Spock should have emerge in the prime just as Nero did.