Very interesting observations. As my bowel incontinence is due in large part to severe chronic constipation, my SCI doc has virtually prescribed me two cups of coffee each morning to "help move things along." That is timed with breakfast to reinforce the gastrocolic effect.
When I have a messy diaper in the morning, it is due to my laxatives + coffee kicking in a bit earlier than I had planned

.
The purpose of the coffee and breakfast is to move as much "stuff" as low in the colon as possible, so that it will be flushed out by my medically-prescribed enemas. Afterward I am almost guaranteed to stay "neat" until the next morning.
I have not sensed a difference from different sources of coffee. I mostly drink expresso from K-cups when at home.
--John
(double incontinent)