I purchased a lot of GE Fluorescent 21W 2D 4 pin butterfly CFL to E26 screw base adapters from e-Bay (like this) and I am now looking at where to source bulbs to use.

The adapter/ballast states it is designed for 120V 60Hz which is what I need as I am in the USA... E-bay seems to be the only place with 2D bulbs in stock, but as I do not want to pay e-Ripoff prices for NOS 2D bulbs, I am looking at Alibaba to source these bulbs as China appears to be (probably the only place) still manufacturing them and they can be purchased for only a couple dollars each. The Chinese manufacturer lists their 21W bulb as designed for 220V, but is 220V a requirement that matters to the tube? I would think that the voltage listed on the ballast/adapter is more important, and that having the correct wattage on the bulb is most important for that component?

Seeing as how GE Lighting was manufacturing 2D bulbs in Great Britain for Europe, where voltage is 220V, I am assuming that the bulbs themselves do not need to run on a specific line voltage as long as the ballast/adapter is providing the correct power input. Further supporting that assumption is the fact that the GE Lighting packaging for NOS 2D bulbs only makes mention of wattage, not voltage or frequency. My guess is that the manufacturer on Alibaba listed the bulb as 220V because more of their customers utilize that line voltage, but that the bulbs would work on 120V line voltage.

Am I correct in my assumption?

To address any questions as to why I am looking to use this type of bulb and ballast specifically: I have ceiling-mounted ceramic fixtures in my basement which I would like to light with fluorescent lighting. Self-ballasted CFLs should not be run ballast-up, so my options are: 1) buy a Circlite E26 adapter/ballast and use Circline bulbs or 2) buy a 2D Butterfly E26 adapter/ballast and use 2D bulbs. I found it extremely difficult to find a large amount of Circlite E-26 adapter/ballasts for sale at a good price, but I was able to find these 2D E-26 adapter/ballasts for a good price.

The bulbs run on a specific current that is supposed to be regulated by the ballast and then the bulb is what dictates the voltage.The lamp does require the ballast to reach certain voltage when not loaded, in order ro ensure stable arc (usually around 2x the arc voltage).
So at "first level" it is the ballast that needs to be designed for a given mains voltage, not that much the lamp.
But the relation between the lamp OCV requirement vs the mains voltage determines how complex, so expensive and lossy the ballast will be.
The simplest is a series choke, but that limits the lamps voltage range given the mains. So woith many lamp families there became two lamp versions for otherwise the same use-specs, one with lower arc voltage but rated at higher arc current for 120V market and second with kigher voltage and lower current for 230V markets. Examples are PLS13 vs PLS11 (both around 900lm PLS style sticks), US vs European HPS for power levels 150W (S55) and below (there the US has both variants, as the higher voltage one offers so much better performance it offsets the higher ballast cost and losses).

So with these lamps you need to check whether they really are the same specs.

Later electronic ballasts were able to operate even the higher voltage lamps with not much extra cost and losses, so with an electronic ballast the higher arc voltage lamp isn't that much problem anymore, so lamps designed for electronic only are then usually not differentiated between the mains voltage markets.