Got a bigger question, given how big the Romulan empire is as remembered. Why didn't the Romulan government did the rescue themselves, they got the ships, they got the worlds, and if as stated from the series, the condition of the sun beforehand, and it sounds like it was. The Romulan government could have taken care of that on their own.
As for Starfleet, it has been pointed out, when things get wonky...they look to get out of it. This behavior was present in all previous Tv series and movies.
Well, we know they asked the Federation for help, so I conclude that they did not have the ships.They had ships, but not enough.
I am not entirely sure the figure of 900 Million people is how many they had in total on the planet, or is how many they couldn't evacuate on their own.
A thing to keep in mind about the Romulan Star Empire is that they rely heavily on cloaked ships. Their individual ships don't seem weaker than the ships Starfleet has, so if they were equal-sized in fleet, there is absolutely no reason why they shouldn't be able to steamroll them, because with cloak, they can decide to only engage at weak spots and their target must spread its resources to be ready for attacks at any spot in their space.
But they never even try, they always use rely on subterfuge.
And in Yesterday's Enterprise alternate timeline, we see that they were overrun by the Klingons - decades after the Praxis incident, which put the Klingon Empire in a weakened state, so weak that they needed peace, and even an alliance, with the Federation to manage.
So my take is - the Romulan Empire doesn't have a huge fleet at its disposal, at least not compared to the Federation or the Klingon Empire. They use cloak to only strike when they see a huge opportunity open up. They cannot afford a prolonged war, however, because they can't defend their Empire once an enemy goes really on the offensive and is willing to sacrifice some worlds.
Their strategy works for them most of the time.. But when it comes to evacuating a planet, it's not about tactics or strategy, it's about raw numbers.
This has ALWAYS been the problem with Star Trek. You have all these different races that have been space faring for centuries, if not millennia before the humans get out there, and, yet, in a very short span of time, not only have the humans caught up with everyone, they've flat out surpassed most of them. It doesn't stand up to a moment of scrutiny and it's one of those things you just have to completely ignore in the show.
But it's not just the humans that's catching up to everyone. It's the Federation. I think the humans are maybe the magic glue that makes the Federation work, and the result is multiple races working together. It allowed them the Federation to overcome challenges that had stumped individual races for centuries or millenia, but once you mix the different viewpoints and approaches of the different species, you can overcome more problems than ever. When your Vulcan gets stuck on his logic, a Tellarite's temperament might make him take a seemingly illogical step and find an unexpected solution, but the Tellarite might just get too frustrated with a very complex and involved math problem that he has to really think through from all the angles and requires an incredible amount of other math problems to be discovered, where a Vulcan logic and patience might allow him to go systematically through it all.
At least that's my take.