Does white stay with white and red to black?
Yes, in North America on a fluorescent ballast, white is neutral and black is hot -- switched hot, that is.
In North American wiring, white and gray are neutral, green and yellow/green are safety ground, and everything else is hot. So red is hot.
Further, there's a mild preference to use black for always-hot and red for switched-hot. You obviously want switched-hot to a light.