Well, that's pretty strange, isn't it.

Pardon the absurb question, but there is no chance the bulbils are late-developing immature seed-heads? Because you say the bulbils are green and very small, whereas by this time of year one would expect them to be well-skinned and cured. It's hard to imagine how a bulbil of a top-setting onion would find its way into a commercial seed-propogated set-growing operation.

I had this happen twice in 4 seasons. However, both times there were just 2 to 3 bubils and the rest seed bloom. Don't know what triggers it but expect that stress of some sort is likely. Since they are clones, the bubils will be the same as the original bulb. Still, would be worth keeping them separate and growing the bubils and bulb out and see if you continue to get bubils or seed next time. Let us know how it comes out.

Both times this happened in my garden the head of bulbils had no flowers. I have a PhD in genetics, but have not done any scholarly work with Allium. I will try to remember to Google using the Scholar version.
The bulbils are in prime condition; not shriveled or damaged. Head is normal; not deformed. The first time, I think the sets were Ebenezer, but this time the grown onions are flatter than Ebenezer. I assume it is some contaminant in the commercial sets. First year I got sets from Jay C, a Kroger company, and in 2006 I got the sets from Haub Hardware which got the sets from Bunton Seeds of Louisville KY.

Is it possible for some 'wild' species of top-setting onions to infiltrate the onion fields of set-growers? That would explain it, though one would expect such a set to look fairly different from the others.

I may lose my topsetting yellow dry onion. Half the topsets have dried down so much, I fear they are dead. once they were 1/8 inch diameter, but now the smaller ones may be dead.
What is the best way to save onion sets? I am contemplating.
1. hang them in a superb damp root cellar that never freezes and is usually 35 to 45F.
2. Plant some in ProMix BX in an growing box where I am growing cabbage plants and it has grown fine plants many years.
3. Keep tham in the kitchen where they have been since July
4. Plant them in garden which ranges down to 10F most years butgets below -10F 1/5 of winters.
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I planted some of the topsets in garden at Thanksgiving and I still have the original 2-inch diameter dry bulb and it looks sound, but has lost about 1/4 of its weight.
Harold Eddleman