I find it curious that the relevant part of CNRTL/TLFi’s entry for “violette” does not include “doigts de” in either the “éventail” or the “bouquet de violettes” version of this expression, whereas that same resource’s entry for “pied” does include these two words in both versions. (cf: OPs link to Expressions Françaises’ definition of the expression in question where “doigts de” is not included in the “bouquet de violettes” version while it is found in the synonymous, “éventail” version)
Although what I find to be curious more often than not eventually turns out to be better described as being “curiously insignificant,” this particular “curiosity” nevertheless did prompt me to examine other French expressions that include the notions of foot/feet and toes and whether using “toes” instead of “feet” or even whether using “foot” instead of “feet” makes a significant difference in the meaning of those other “foot-related” expressions, all in the faint hope of trying to determine if those significant differences, if any, in the other expressions might arguably apply to the expression in question.
Admittedly, the results of my examination have also prompted me to limit my response to a possible explanation of the origins of only the “de doigts” portion of your expression (and not that of the entire expression as you requested), but perhaps the following will help inspire you or future responders to arrive at a fuller answer:
Although the English notions of “putting one’s feet up” and “putting/w[r]iggling one’s toes in the air/sand” could capture the non-sexual, “grande relaxation” sense of the expression at issue and “throw[ing] some toes in the air,” as explained by crude example in The Urban Dictionary, even seems to capture its sexual meaning, the purpose of mentioning these English notions is not to connect them to the subject expression.
I mention them instead as a way of introducing the French notions (and the significant differences between them) of:
1) having “les pieds en l’air” (arguably a decent literal translation of “putting one’s feet up=relaxing);
2) having le/un pied en l’air” (=being restless=+/-“having one foot out the door”); and
3) having “les doigts de pied en l’air” (=being dead/deceased=”toes up”).
All that to say that there is at least some basis for arguing that small, seemingly insignificant changes in and additions to French expressions, at least ones involving our foot/feet and toes, can drastically alter their meanings and that therefore the (curious) existence of two variations of the expression in question (and its synonym), one with “droigts de” and one without, could possibly beg the question of whether the version with “doigts de” has the exact same meaning, and more importantly for this question, whether it has the exact same, unextended roots as the version without those two words.
Granted it’s a stretch (as are most of my “answers”), but just as adding “doigts de” to “avoir le/s pied/s en l’air” seems to change the meaning of those expressions from either “restless” (in the singular) or “relaxed” (in the plural) to “dead” (which is arguably either the exact opposite of “restless” or the ultimate state of relaxation), perhaps the explanation for the addition of those two words in some cases to “avoir le pied en éventail/bouquet de violettes” could be traced and related to an attempt to emphasize the distinction between the general, “feet-in-the-air, non-sexual state of grande relaxation and the near-death, “toes-in-the-air” state of sexual “relaxation” or climax, which latter state has been aptly described as and likened to “la petite mort” by both French and English authors since, if I’m not mistaken, Edmond de Goncourt first used “la petite mort” in this sexual way in La Faustin in 1882.