There is a tense and punctuation problem. I suggest The program rounds up to the nearest hour. If you logged in at 5:47 p.m.,it would round up to 6:00 p.m.
Ever so slightly, I think I would prefer "nearest" - but your version is OK. I would change the second full stop and, to make the meaning quite clear, you could mention the hour...
- The program rounds up to the nearest hour. If you've logged in at 5:47 pm, it'll round that up to 6:00 pm
(Actually, to make it quite clear, you should say what