As per the title, does Time Machine back up DTPO when it’s open or does it need to be (or is it better that it’s) closed.
I generally have it the external HDD plugged in when I’m at the desktop and let it do its stuff according to its schedule, but am I negating the point of the backup if DTPO is running when the backup is being made?
No, it doesn’t have to be closed. Time Machine works in a snapshot style fashion, so it captures the data from a point in time, not a continuous stream of backup data. (And yes, this is the best and most data-safe method with our databases in the backups, part of why we advocated it.) The changes you make while a backup is running will be captured on the next backup, in an hour if the drive is still connected.