Y’know, kids, there’s no such thing as a whole planet that experiences only daylight if it has just one primary (sun). It may have perpetual daylight on one side, if it doesn’t rotate, but that means it has perpetual night on the other side (and an inhospitable climate and serious atmosphere problems, but that is beyond the scope of this blog post).
Daytime isn’t exactly the same as daylight, and I think the distinction is relevant here, so replace daytime with daylight.
Move only so it’s before daylight. (Yes, this matters. Otherwise, you’re saying it experiences daylight but doesn’t do anything else with it, but what I’m sure the writer meant is that it experiences nothing but daylight. See the difference?)
Add a comma after daylight, because the sentence is compound.
I think their should be replaced with its. The sentence is about the star and the planet, not about the views of the planet’s (presumed) sentient inhabitants.
As for the science aspect… I see no way to fix this without either making major changes to the described setting or assuming the perpetual daylight applies to the inhabited part of the planet, rather than to the whole planet.
A distant planet experiences only daylight in its inhabited zone, but suddenly its star sets on the horizon.
Eh. Still don’t like it. Some story concepts just don’t work. Yes, I am familiar with Asimov’s story dealing with a planet that rarely experiences full darkness: the novel, the short story, and the movie. This is not the same situation, because Asimov’s planet had multiple suns.