In the wikipedia article on spot color:
In offset printing, a spot color is any color generated by an ink
(pure or mixed) that is printed using a single run. [CMYKOG...] The
two additional spot colors are added to compensate for the ineffective
reproduction of faint tints using CMYK colors only. However, offset
technicians around the world use the term spot color to mean any color
generated by a non-standard offset ink; such as metallic, fluorescent,
or custom hand-mixed inks.
Beyond contemporary dictionaries (Oxford, Dictionary.com), the PrintWiki - The Free Encyclopedia of Print provides interesting details on spot color (a specific region of a printed sheet - so a "spot" as you say - and the fact that there is no need for color separation i.e. by contrast to how process colors are used, etc.) and furthermore states that it is sometimes called a tint:
In printing, an alternate term for flat tint. See Flat Tint.
The term tint is also occasionally used as an alternate term for spot
color. See Spot Color.
In subtractive color theory, tint refers to a primary hue to which
some quantity of white pigment has been added.
The term tint is also an alternate term for saturation, or how white
(or light) a particular hue is. See Saturation.
In ink mixing, a colored printing ink to which a quantity of extender
or white pigment has been added in order to reduce the color strength
of the primary color.
In halftone photography, tint refers to a halftone produced with a dot
percentage of less than 100%.
Etymology (Online Etymology Dictionary)
c.1200, "moral stain," probably from Old English splott "a spot, blot,
patch (of land)," and partly from or related to Middle Dutch spotte
"spot, speck." Other cognates are East Frisian spot "speck," North
Frisian spot "speck, piece of ground," Old Norse spotti "small piece,"
Norwegian spot "spot, small piece of land." It is likely that some of
these are borrowed from others, but the exact evolution now is
impossible to trace.
Meaning "speck, stain" is from mid-14c. The sense of "particular
place, small extent of space" is from c.1300. Meaning "short interval
in a broadcast for an advertisement or announcement" is from 1923.
Proceeded by a number (as in five-spot) it originally was a term for
"prison sentence" of that many years (1901, American English slang).
To put (someone) on the spot "place in a difficult situation" is from
1928. Colloquial phrase to hit the spot "satisfy, be what is required" is from 1868. Spot check first attested 1933. Adverbial phrase spot on
"completely right" attested from 1920.
mid-13c., "to mark or stain with spots;" late 14c. as "to stain,
sully, tarnish," from spot (n.). Meaning "to see and recognize," is
from 1718, originally colloquial and applied to a criminal or
suspected person; the general sense is from 1860. Related: Spotted;
spotting. Spotted dick "suet pudding with currants and raisins" is
attested from 1849.
"color," Old English hiw "color, form, appearance, beauty," earlier
heow, hiow, from Proto-Germanic *hiwam (cognates: Old Norse hy "bird's
down," Swedish hy "skin, complexion," Gothic hiwi "form, appearance"),
from PIE *kei-, a color adjective of broad application (cognates:
Sanskrit chawi "hide, skin, complexion, color, beauty, splendor,"
Lithuanian šyvas "white"). A common word in Old English, squeezed into
obscurity after c.1600 by color, but revived 1850s in chemistry and
"color, tint," c.1600, from Latin tinctus "a dyeing," from tingere "to
dye" (see tincture).
c.1400, "a coloring, dye," from Latin tinctura "act of dyeing or
tingeing," from tinctus "dye," past participle of tingere "to tinge,
dye, soak in color," originally merely "to moisten, wet, soak," from
PIE root *teng- "to soak" (cognates: Old High German dunkon "to soak,"
Greek tengein "to moisten"). Meaning "solution of medicine in a
mixture of alcohol" is first recorded 1640s. The verb is recorded from
1610s. Related: Tinctured.
So the noun can mean amongst other things something close to "compliant" or "be right". The verb can mean something close to "fill" as well as "identify". Historically, hue comes before color and tint involves some type of process.
U.S. Very late 19th (The Century Dictionary, 1890s)
This source details many meanings of spot, but it contains no reference whatsoever to spot color. Yet the supplement contains spotter used differently than in the main work(one who spots, a detective):
[...]4. One who tints photographs.
So could there be some relationship to a specialized field of that era i.e. tinting of photographs, where [a] single overall colour underlies the image and is most apparent in the highlights and mid-tones? See also hand coloring. In Dictionary.com there is also a photography-related meaning, but in a different light, as in spotting(retouching): to remove spots from (a negative or print) by covering with opaque color. So a spotter colorizes whereas spotting involves small patches on specific spots for retouching.
Quick comparison: French
The French version of the article on spot color is called "Ton direct":
Le ton direct en imprimerie est le fait d'imprimer une teinte
directement sans passer par l'utilisation du spectre CMJN.
That word is tint, from the same latin origin. The English language is trying to express something like "to print a tint directly". The context is hue had been replaced with color historically. So is it a "spot on/for the spot/on the spot/hitting the spot" color in reference to that too i.e. of a specific tint/for a specific print job/directly/complying with expectations? It certainly seems to be about "peculiar parameters" for an ink tailored to a job so as to enable a simpler print process.
This exploration supports no conclusion. Observations could be that it seems a lot about colors for specific "spots" like you said. At the same time, the word spot has a rich texture. Photographic techniques are central to modern 20th century printing and the study of color from the middle of the 19th was key in specializing/rediscovering words related to color and developing processes. At that time, a spotter used to be someone who tinted photographs - in some cases by hand. The idea of spot color may also be independently linked to an exact tint and that is somewhat related to a "direct" process which contrasts with printing using transparent inks i.e. by layer.
Hopefully this can assist someone with expertise in connecting the spots!