What does directly commonly mean in standard AmEng when used as a temporal adverb,
immediately/instantly/at once/right away/without delay
-or-
soon/shortly/in a little while?
DIRECTLY
At once; instantly: Leave directly.
Chiefly Southern US In a little while; shortly: He'll be coming directly (emphasis is mine.)
American Heritage Dictionary of the English Language
At once; without delay.
Shortly; soon.
Usage note:
immediately, instantly, directly, presently were once close synonyms, all denoting complete absence of delay or any lapse of time. immediately and instantly still almost always have that sense and usu. mean at once: He got up immediately. She responded instantly to the request. directly is usu. equivalent to soon, in a little while rather than at once: You go ahead, we'll join you directly.
Please, consider:
Have a seat, Dr. Campbell will be with you directly.
She fell asleep directly after she went to bed.
Does that mean,
Dr. Campbell will be right with you/will be with you right away/with no delay.
She fell asleep immediately/right after she went to bed.
-or-
Dr. Campbell will be with you shortly/soon/in a little while.
She fell asleep shortly/soon after she went to bed.