The expression means, essentially, after something unpleasant (represented by a medicinal powder), a restorative treat (represented by jam).
The earliest Hathi Trust match involving text that conjoins "powder" and "jam" is from a review of The Interrupted Wedding," in The Saturday Review of Politics, Literature, Science and Art (December 5, 1863):
It [The Interrupted Wedding] is neither history nor fiction, but both; and the two elements are clumsily combined, or rather there is no combination at all. The historical portion and the imaginative portion mix together as ill as oil and water. The only apology for an historical story is a careful working up of truth with fiction, a thorough incorporation of the powder with the jam; but the Interrupted Wedding is so clumsily arranged that, after taking a little mouthful of the jam, we ruefully discover a great lump of dry powder left in the bottom of the spoon. The critic has no choice but to swallow it, but we very much question whether the voluntary reader will submit to the process with equal resignation.
The image is of a sweet substance (here, fiction) used to mask the flavor of a bitter or otherwise unpleasant one 9here, history). In this first instance, the juxtaposition of powder and jam is immediate, but the expression in Agatha Christie's Hickory Dickory Death (1955) suggests a different approach, where one swallows first the unpleasant powder first and then the much better-tasting jam. An example from "An Open Letter to Mr. W. H. Msallock," in The Academy: A Weekly Review of Literature, Science, and Art (April 9, 1898) uses this formulation:
You will say that it is very rude of me, your unknown correspondent to damn your novels (except The New Republic) and your verse with this faint praise, but there is still another department of your work which remains to be spoken of, and of that I can write with very much greater favour. After the powder, the jam; after the Human Document and the poems, I come to those sociological and philosophical writings of yours which I always read with pleasure for their clearness of thought and precision of statement.
From an untitled item in the [Penrith, New South Wales] Nepean Times (April 23, 1904):
The Lady Minister.—After the powder the jam. Repulsed from the (legal) Bar, woman has forced an entrance to the pulpit, despite horrid masculine prejudice, and in Miss Gortrude von Petzold we hail the first feminine minister. Large congregations flock to hear her. But what do the young ladies of the congregation think of it? A picture arises before us of piles of half worked slippers, and—but the vision is too heartrending for words.—[London, England] 'St. James' Gazette.'
From "India Again" in The Saturday Review of Politics, Literature, Science and Art (April 26, 1913):
Three books written from three totally different standpoints (one an American) we have just read. Of these one may be at once eliminated from the class of desirable books about India, for it is not only unpleasantly written and in a tone of bitter unconcealed dislike of the Indian Civilian (who is invariably referred to as ;the bloated Civilian" (!), apparently on account of his receiving a Government pension and higher pay that the so-called "uncovenanted Civilian" to which class the author announces himself as belonging), but the greater part of it is taken up in merely indulging in imaginary scenes and dialogues between imaginary characters, and these last of an unnecessarily unpleasing and often "impossible" type; of real information there is hardly any, and barring the photographs, which, including one of the author, seem to be quite good, the book may be put "on the shelf" without any great loss to the public. After the powder—the jam! and it was with pleasure enhanced somewhat by going through the previous volume that we read Mr. Palmer's "Little Tour in India". This is a collection of letters, not written originally “for publication”, as the author says in his modest preface, and the letters show that the writer is a keen observer both of the people and the scenery among whom he travels, and that he writes what he thinks about them.
Hathi Trust also reports examples of "after the powder the jam" from 1933 (in The Month, volume 162) and 1937 (in James Curtis, There Ain't No Justice)—but it does not show the relevant text in either case.
All four instances cited above from the period 1863–1913 are from British sources (although one was picked up and reprinted by an Australian newspaper), suggesting that the expression originated in England