I don't think you have to take the kitten home, but you can't just throw a kitten or any cat in with a resident cat without a slow introduction process.
If you are only emergency sitting, simply always keep them separated until the kitten leaves..Though I am not quite sure of the reason you are "kitten-sitting".
No, your co-worker doesn't seem to have all the correct info.
Sometimes same sexes or opposite sexes get along just fine..It all depends on the cat and the age and activity level as well as how well introductions were handled.
Let us know what you decide!!!
But for now, keep them apart.