Why is this a protip? What does putting it on before or after putting a shirt on do? Sounds like personal opinion, and not a clever technique to accomplish an old task.
invisible already stated that a dark shirt and white non-gel type deodorant will most likely result in a rather embarrassing slash down the side of your shirt. One that I have been a victim of more than once. Seems like a good enough reason to get in the habit of applying it after putting on your shirt.
The rest is just routine: new day -> new shirt; fresh cloth -> deodorant; sunday -> do laundry..