The big issue here is that Spock apparently set out to save both Romulus and the galaxy, as if one wouldn't exclude the other. He failed with Romulus, but we don't have much reason to think he failed with the galaxy (he did start a "return trip", which would make zero sense when Spock is the sole and exclusive savior of the galaxy).
It's just that we don't really know what red matter does. Spock says he wants to "create a black hole" to "absorb the exploding star" by shooting the red matter "into the supernova". But what we see is something different altogether: Spock ejects the vial of red matter, which then turns a portion of the expanding wavefront of menacing rubble into pure fire, in a ring that then starts to spread across that wavefront, at the very least punching a massive hole in it and possibly removing it of existence altogether.
And what we hear happens is different still: a hole through time is created. Perfect for putting Humpty Dumpty back together again?
So we are left completely in the dark about what exactly Spock hoped to achieve within the "little time" he had; whether he did achieve that; and what it means for Remus, which would be on his to-do list of things to be saved with red matter, no matter how implicitly.
Of course, there's an even darker option open. Spock never says he intended to save Romulus. He just considers it "unthinkable" that the planet blows, but OTOH this happens while he is still en route, and it seems odd that he would calculate wrong. Perhaps he always intended to save the galaxy by sacrificing the Romulan star system? In that case, Remus would not be the reason why he makes the effort for which he has the "little time". And its salvation would be an unlikely collateral outcome.
Timo Saloniemi