This is relatively far from my area of expertise, but I'll give it a shot. The only passable source that Wiki gives on the history of pincushions is Gertrude Whiting's Old-Time Tools & Toys of Needlework, originally from 1928. She traces the first references of "pyn-pillows" to the sixteenth century, and notes in passing that "most of us are familiar with the red flannel, tomato-shaped cushion." That's pretty much all she has to offer us, and most internet histories of the tomato-and-strawberry pincushion are filled with unsourced claims about supposed folklore whereby a tomato was placed on the mantel of a home to ward off evil spirits. (Whose folklore? Nobody seems to know.)

In the Victorian era, pincushions fell into the category of sewing-aid objects called "fancywork" or "fancy goods," and one of the few reputable scholars I can find who has done significant work in the amazingly specific history of fancywork is Beverly Gordon—here, for instance, is a brief article of hers on Victorian fancywork. She mentions tomato pincushions in her article "Victorian Fancy Goods: Another Reappraisal of Shaker Material Culture."

First, a bit of background on the Shakers. For those who are unfamiliar, the Shakers were* a Christian sect based in New England notable for their celibacy, isolated communities, ecstatic worship, beautiful music, and high-quality handmade crafts of various kinds. (*Technically they still exist, but there are apparently only three of them left—their celibacy is rather detrimental to their continued existence.) According to Gordon, Shaker communities were becoming more integrated into the American economy in the 1860s for a number of reasons: they had figured out that it was far more efficient to focus on certain crafts for trade purposes than to remain completely self-sufficient, and thus dramatically increased their production of certain objects like furniture and fancywork; also, the establishment of railroads and the burgeoning postwar economy (both part of what some call the "Second Industrial Revolution") increased tourism and trade in their communities. Partly due to a nearly 3-to-1 female-to-male ratio in their population, the Shakers began to produce more "women's goods" like fancywork, which became one of their most profitable sectors, and the one for which they were best known at the time (as opposed to furniture, the sturdier products for which they are best remembered today).

In contrast to most women's goods of the time, the Shakers eschewed ornament, ostentation, and ephemerality in favor of the functionality and simplicity that their theology demanded; therefore, their fancy goods lacked the imitative and representational quality that was common among their mainstream counterparts. Gordon writes of the latter: "A tape-measure dispenser appeared in the form of a coffee mill; a pincushion appeared as a bellows or a shoe or a fish; a pen wiper was made to look like a sheaf of wheat. [...] In short, non-Shaker fancywork was 'cute' and entertaining; it was sentimental and childish." Shaker goods looked like what they were, and the Shakers therefore did not make pincushions that were decorated like tomatoes; however, the tomato shape became common in their pincushions. Gordon writes: "Eventually, simple scallop-shaped needle books; round, or tomato-shaped, pincushions; and conical, or strawberry-shaped, emeries emerged as standard forms and were regularly included from the 1870s on." (This source mentions "tomato cushions" as early as 1861 as a product of the New Lebanon, NY Shaker community.) The "tomato shape" refers specifically to a cushion with six or eight segments sprouting from the center in a circular fashion, like this, which looks a bit like a horizontally-sliced tomato, I guess. Gordon does not speculate on why this shape should have become a standard form. I know very little about sewing, but I would note that this same segmented division has been retained in modern tomato pincushions—perhaps it's useful to be able to keep track of different groups of pins?

The point at which the tomato-shaped pincushion became the pincushion-disguised-as-a-tomato is not clear, but it was presumably a mainstream adaptation of the Shaker tomato cushion, in keeping with the imitative fancywork mentioned earlier. In her article "Victorian Fancywork in the American Home: Fantasy and Accommodation" (found here), Gordon writes:

All ornamented fancywork was beneficial, but instructive objects that manifested qualities of the natural world and brought its edifying lessons into the family parlor were particularly helpful. Fancywork constructed or embellished with shells, fish-scales, moss, pine cones, seaweed and similar materials can be understood as domestic expressions of a Victorian interest in natural history.

Just one more quick source: Virginia Mescher's article "The Case of the Lost Thimble: Work-Boxes, Work-Baskets, Housewives and Traveling Sewing Boxes," which has a useful bibliography and extended quotations from 19th-century domestic guides. Of particular interest is the following bit from L. Maria Child's The Girl's Own Book, from 1834 (the date is important):

Another toilet cushion is very pretty and convenient, made of bits of ribbon so as to form a six-sided circle. [see picture in article] The little hole in the center is left hollow. The pearl edges of the ribbon are stitched together at the outside. The edge is left perfectly straight; the pretty scalloped appearance is merely a little jutted out, where the slanting edges of the six bits of ribbon are sewed together. The beauty of the shape depends a good deal on its being stuffed full, plump, and even.
[...]
Emery-bags are made in various forms. Some are merely little square bags, stuffed hard with emery; others are made round, and painted like an apple, plum, or peach; others imitate a little barrel, with cord put round for hoops. But the prettiest are imitations of strawberries, made of crimson merino, worked with green and brown silk to represent the calyx and spots of the strawberry.

The first paragraph seems more or less to describe the shape of what would later be called a "tomato cushion." The second paragraph indicates that emery bags were already being made to look like strawberries 25 years before the Civil War. These pieces of information are important for dating purposes, but I don't think they invalidate the idea that the Shakers were responsible for standardizing and popularizing the tomato shape and, perhaps more importantly, the name, allowing subsequent nature-loving Victorian housewives to take the last step of actually making it look like a tomato and joining it to the strawberry emery bag.

TL;DR The imitation strawberry emery bag appears to date from at least 1834, as does the shape (but not the name or decoration) of the tomato pincushion. The tomato name seems to have come from the Shakers, who standardized and popularized that shape of pincushion in the 1860s and 1870s. Sometime in the ensuing decades, the tomato pincushion gained its decoration and joined with the strawberry in a persistent and fruitful union.