"Directly" in the meaning of "As soon as"

As reported by the NOAD, using directly to mean "as soon as" is British English usage.
Directly was once used to mean "in a little while, soon"; this use was common to American and British English.

She fell asleep directly she got into bed.
I'll be back directly.

This usage isn't (quite) obsolete, in Britain at least, but is relatively formal and associated with a 20th century RP mode of speech and writing, which tallies with the Fleming source. Related to your examples is its use to mean 'in a short time', as in 'I'll be with you directly,' and the nice Cornish word dreckly.

Growing up I was more used to "directly" being used to mean at some indeterminate time in the future. I understand now that the correct dictionary meaning is "as soon as" or "at once", but my Mother and some other adults I used to know used it to to slow down an expectation (more in line with the definition above of "soon, in a little while"). Interesting how a word can be turned around to mean almost the exact opposite of what the actual definition is.

I live in Texas and I remember my great-grandmother, born in 1907, regularly used it to mean "in a little while". Anytime she was leaving, "I'll be back directly" (pronounced "dreckly"). Anytime she was coming, "I'll see you directly" (again, "dreckly").