Measuring time is something we take for granted these days, but thinking back, it must have been a solution to a problem we faced long ago. We decided to create a measurement system that accurately predicts the sun's movements because we're a daylight reliant species who sleeps at night and grows food. Our planet has seasons which greatly affect our daily lives.
Now, imagine if we were to suddenly become immortal and we lived until well past the life of our original sun. How would that change our need to measure time? I'd imagine we'd keep the sun date system on some other planet (perhaps keep track of our original sun for posterity and phase in a second sun based time system). We'd likely mimic the familiar Earth time in any colony we make as well.
Therefore, the way to figure out how this immortal species tells time would be to ask practical questions and go from there.
- Did they start out on a planet like Earth?
- Do they sleep? If so, when?
- Do they or have they ever relied on agriculture?
- Do they or did they ever live on a planet with seasons?
If they don't sleep, eat food they grow or live on a planet with seasons, time can still be important, especially if they're a social species that doesn't have a hive mind (or is strongly telepathic). Regardless of whether they're immortal, they must operate with a frame of reference. That frame of reference can be temporary, especially if it's extraordinarily long lasting. If it is, they would likely have a system in place to choose another temporary frame of reference that is identical. They would choose something apparent and important, ideally.
That being said, I hear that white dwarf stars are incredibly long lasting. Their lives are said to be as long lasting as the universe. However, they're terribly dim and hard to see. I also don't recommend they replace a moderately sized star like our sun because it would be too cold, and the only planets close enough to have warmth similar to ours would be locked facing it, causing eternal day on one side and night on the other. Still, if one were available to view in the night sky far away enough that it doesn't lock the planet's rotation but also traveling in roughly the same direction and speed in the universe, it'd have potential to be a permanent frame of reference, especially if mapped from a rotating and spinning planet/colony ship. But I can't tell you how that would be practical.
I wish I could give you a more directed answer, but considering I know so little about this immortal race, it's the best I can do.
EDIT: Since I've obtained more context, I'm going to get more specific (while leaving the original answer intact).
Able to manipulate space-time, including the ability to convert matter
into energy and vice versa
Considering they control space-time, it sounds to me like accurate time is both immensely important and not important at all depending on circumstance. Is this a technological advance? If so, then they'd likely solved the time measurement long before they learned how to manipulate time and perhaps revamped time measurement after the invention, and would therefore have two separate measurement systems (much like we have different measuring systems for temperature and size). The Gallifreyans of Doctor Who (also time-space manipulators with long lives) seem to have a universal time-line based between the big bang and the final collapse. They use important events as markers and have even developed timeline related senses.
Originate from empty space, but built a planet to serve as their "home
If not originating from a planet I cannot begin to guess at their physical size. (To be fair I can hardly guess their size if they had!) I'm supposing ants would measure time very differently from humans and if a galaxy were sentient it would measure time with a completely different (and impractical by human standards) system. I'll give the benefit of the doubt that these creatures are a size that can fit on the Earth and most other planets (AKA they're minuscule compared to a star). A point of reference would be what they base their time on, whether it be a migration, a star life or some other significant repeating event. I'm also going to assume they require energy of some sort, and therefore rely on stars, at least to a point. So some time system based on stars would make sense, even in absence of the context of a planet.
Capable of sexual reproduction
Sexual reproduction is often a sort of lifecycle event based in other natural cycles. What sort of lifecycle do these immortals have?
Do not sleep, but do possess a rest cycle that accelerates healing
The rest cycle is likely based on periods of inactivity and peace. Time measurement would take active events that interrupt inactivity and peace into account. The immortal beings would need to plan ahead in order to facilitate the rest cycles.
Can consume material food, but can survive indefinitely on stellar
They require stellar energy and would therefore find the lifecycle of stars extremely important. Their time would likely be based on that much like ours is based in seasons.
Interact with mortal races on a regular basis
If they interact then they would likely influence and be influenced by these mortal races. (Again, see Gallifreyans for comparison.) It is therefore possible that they can use the mortal time measurements for sake of the mortals. This is additionally feasible considering they are generally not the main focus of the story.
Can view 90% of the light spectrum and limit vision as much as desired
They seem heavily specialized in the light spectrum, which further illustrates that they'd likely base time on the lives and events of stars. Even if it were temporary, like "[Star Name] Era, [Lifecycle state]". When a star dies would be exceedingly important and noticeable.
Can see into the future in near real time
If this is an innate ability, they would likely measure time in events. Time's relative nature would be reflected in their measurement system. Our time is relative too; we have timezones and leap years and even have to adjust the clocks of satellites to fit our time. Time is relative. Time is not fixed. It does not contain an absolute, concrete and measurable attribute. Considering they're immortal and well aware of the transient nature of time, their time system might become more flexible than ours to account for it.