In the 'Passengers' universe Arcturus is only (approximately) 20 light years from Earth.
We can be certain of the ship's flight time because the map room tells us
Jim: Wait. How long ago did we leave Earth?
Maproom computer: Approximately 30 years ago.
and we can be certain of the ship's location because when Jim uses the (laser-based) Comms Terminal to contact Earth, it tells us
Computer terminal: Message will arrive in 19 years.
and we know that the ship is traveling at approx .5 of lightspeed because the ship's Flight Engineer tells us
Gus: We're doing 50% of lightspeed.
Given that Jim is awake for approximately one year before waking Aurora and Aurora is awake for approximately one year before Gus wakes up, at most they could have traveled a further 1-2 light years before the ship slingshots around Arcturus.
That being said, it's possible that the ship accelerated dramatically (see below) after they fixed the onboard computers. This would have have allowed them to reach the real Arcturus in a shorter period.
The ship must have been traveling at a higher speed before Jim woke up.
We know that the ship must have been traveling at a speed greater than 75% of light speed for the first leg of its journey (in order to have traveled 19 light years in just 30 years) and that the Avalon is presumably slowing down, possibly due to the magnetic ramscoop encountering space dust to feed the engines or possibly as a result of the accident that woke Jim. This would also explain the need for a mid-course slingshot to increase their speed.
Obviously none of the above tallies with what the film's writer, Jon Spaihts said about the accuracy of the physics of the film.
Q: There was one reference to a star that the spaceship was making a
slingshot maneuver around – Arcturus, I think? Filmgoers might be
thinking to themselves, ‘Now, how far away is that?’
A: “It’s about the right distance away. [36.7 light-years from Earth.]
I think the dodgiest thing about the slingshot maneuver is, I don’t
know how much velocity you can steal from a body you’re passing that
does not have substantial proper motion with respect to a transit
perpendicular to your direction of travel.
“If it’s pretty stationary with respect to you, I don’t think you can
steal a lot of velocity from it, especially if you’re traveling 0.5 c
before you get there. So it’s more of a showy move. It might be a way
of changing your trajectory.”
How screenwriter Jon Spaihts worked the physics of starship travel into ‘Passengers’
At the very least this implies that the ship's speed is highly inconsistent but more likely it's just a straight up goof by the writer.
He did admit to having taken some liberties with our "local neighbourhood". Perhaps this is one of those changes.
"I did investigate our general galactic neighborhood. Traveling at a
fraction of the speed of light for 120 years can't actually get [a
ship] very far; there's really just a basket of stars that they could
be going to," Spaights said. "I had a general notion of where they
might have found the habitable planet, and maybe stretched a little
bit how far they might have gone [to get there]."
Real Science Inspires Voyage to the Stars in 'Passengers'
You might wish to note that in the original script the star was simply described as "a Red Giant", rather than being named as Arcturus.
A STAR looms ahead of the ship: a RED GIANT. The Excelsior rockets
toward the star. The passage takes less than a minute. The Red Giant
swells in the windows. The ship shudders. The engines howl. Aurora
falls into Jim’s arms. The ship bathed in red light.
and the ship's position was far more explicitly confirmed.
COMMUNICATIONS BOOTH: We are nineteen light years from Earth. By the
time your message arrives, we will be thirty-six lightyears from
Earth. We apologize for the delay."