People seem to forget that the colon is attached to the rest of your body and in particular the rest of the GI tract. Lots of things affect your colon's behavior as soon as they enter your mouth (where digestion begins). I believe many here have experienced diarrhea that is triggered by the first bite of food! Surely it's obvious it isn't because that bite is traveling ~22 ft to your colon in ~5 seconds.
Some pretend like it does travel that fast, like when a topical agent is ingested and (deep colon) relief in minutes is claimed.
But otherwise, yes, some spasm response might get directly propagated along the gi tract as a function of adjacent muscles. Other response might take a secondary route, in that it causes secretion/absorption/release (i.e., blood) of something higher up, and then in some systemic fashion (i.e., blood stream, spinal nerves) a lower-GI response is triggered. Most of these types of lower-gi responses will be motility related (i.e., not ulcer/inflamatin) just because of how the signal traveled. This will be more IBS than IBD, yet many seem to get some IBS secondary to IBD.
I think there are also pathways involving the CNS. Some nausea response (either because the substance evokes nausea from delicate tissue, or because the individual has been conditioned to experience nausea after eating) would not be just spinal cord nerves (i.e., refelx-like) but signals would go to the brain (because it is brains that get nauseous) and from the brain all kinds of nerve, hormone, and other chemical signals can go out to cause a fair number of "seeming immediate" responses.
Coffee is much more likely a caffeine-->blood-->colon tissue stimulus pathway. But there could also be causal action for warm beverage, and/or for beverage, and/or for fear/placebo effect of coffee/beverage. Heck there could be some sort of histamine response, which travels through blood from stomach to colon.
It is good to keep in mind that the blood does not travel mouth to butt in 20 minutes (except under extreme-dysentery like conditions). It is also useful to think about
how any response might be happening: is it topical, muscle spasm, through blood stream, how often/likely the brain is involved?