Dispersal of pyrethroid insecticide by vaporization - role of petroleum distillate in distribution in air I live in Indonesia where there are many mosquitoes and products sold for their control.
One such product is this one:

The product contains 22ml of liquid, the contents of which likely vary slightly by jursidiction
https://www.whatsinsidescjohnson.com/ph/en/brands/Baygon/baygon__liquid_starter

Prallethrin - 1.316% (Wikipedia indicates 1.6% in typical products in India https://en.wikipedia.org/wiki/Prallethrin)
Petroleum Distillate (carrier) - Enables the delivery of a product to a surface.
Butylated hydroxytoluene (BHT) - preservative
Fragrances

They sell a liquid for use in a sprayer like this:

Unlike the plug-in which releases very small amounts of insecticide continuously, a sprayer would be sprayed manually perhaps once or twice a day. The product is sold in quantities of around 300-700ml.
Active ingredients vary by jurisdiction: in the Philippines
https://www.whatsinsidescjohnson.com/ph/en/brands/Baygon/baygon__multi_insect_spray_waterbased_refill

Water
Transfluthrin / Cyfluthrin
Isopropanol &quot;wetting agent&quot; - Helps a formula spread across a surface.
Benzyl Alcohol - anti microbial preservative
Sodium Lauryl Sulfate - detergent
Acetyl Tributyl Citrate - Helps ensure even distribution of a product's ingredients.

The Indonesian version is:
https://www.whatsinsidescjohnson.com/id/id/brands/baygon/baygon__liquid_spray_floral

Water
Cybermethrin, imiprothrin, prallethrin
Propylene Glycol Butyl Ether and PEG-60 Hydrogenated Castor Oil instead of the Acetyl Tributyl Citrate
Methylisothiazolinone &amp; Benzisothiazolinone instead of the benzyl alcohol
Ethoxylated Alcohol in place of the SLS

Another company sells a similar liquid product to the Baygon liquid

This is sold in two formulations, the regular and the water-based which notes

'tanpa minyak tanah' (literally 'without ground oil', i.e. paraffin - this is not a very technical term and obviously means that the alternative product contains some kind of petroleum distillate)
Both regular and water-based formulations contain the same active ingredients: 1.14% prallethrin, 0.29% cyfluthrin.
I presume that there are particular properties of prallethrin that make it better for vaporization with an electric plug-in device (which I guess is not close to boiling - this should be evaporation) than certain other pyrethroids, but the question is:

if one were to refill the plug-in device with the 'spray'-type 1.14% prallethrin, 0.29% cyfluthrin petroleum-based product, would it be reasonable to expect it to have similar dispersal effectiveness to the 1.32% prallethrin petroleum-based 'vaporizer' product
given the existence of 'water-based' and 'petroleum-based' products with the same insecticides, is the 'water-based' less effective at dispersal, and does it have any advantage beyond presumably some sort of antipathy towards hydrocarbon vapours for health reasons.
In short:  the petroleum most likely is used as a solvent.
Small detour:  tablets of asperin contain acetylsalicylic acid as the intended active compound.  But the tablets contain other chemical compounds as well, for example to retain the active ingredient in «good shape» (e.g., stabilizers, antioxidants, etc.) and not at last, fillers.  Because, to moderate the wanted action of aspirin in the body, you possibly need a smaller mass of the pure compound, than your balance at home allows you to measure. Thus, the active ingredient is diluted; you equally could say, it is dissolved in the solid matrix of the tablet.
Now to the pyrethroids in question.  Similar to perfume, only a relatively small number of the molecules per cubic foot / cubic metre of air suffices to trigger the action; here, against the insects without triggering nausea / headache etc. to you.  (It is a question of balancing the effects, and the cost producing the materials vs. return of investment for the company, too.)  Thus, the pyrethroids are distributed as diluted.  Given the structures of two of the compounds you mention (they differ)

(prallethrin, source)

(cyfluthrin source
there are no, e.g. hydroxy-groups which could render the substances well soluble in water (hydrophilic).  Instead, they are more likely to dissolve in apolar solvents, such as petroleum is, then called «carrier».  In the other recipe, the PEG and propylene glycol butyl ether may function as the slowly evaporating solvent (mixture).
(Possibly, the list of ingredients was rearranged for this question; often, the containers list them in decreasing relative amount to the total content.)  The list of ingredients from the Philippines still may indicate lots of water in the bottle because simultaneously there are other compounds which may mediate between the polar water and the less polar pyrethroids to yield a solution; especially isopropanol (an organic solvent miscible with water), and the detergent, sodium lauryl sulfate may increase the solubility here.
It may be, that overall the recipe using both prallethrin and a little of cyfluthrin is more efficient or / and is less costly to produce than using the other recipe of prallethrin  alone.  It may be local legislation setting an upper threshold for one, or the other compound differently in one country, to the other; which may be to protect you directly as a consumer, or the environment in general (they don't decompose well in normal wastewater treatments and thus may enter the food chain).  Because the evaporation of an aqueous solution may well differ from one based on petroleum, it is not evident that one may be used to refill the other in the electric nebulizer.