I realize that with summer onions I wait until the leaves die off and fall over - are these the same? Someone told me I harvest them in June and its June.

If they flowered, they won't fall and sad to say, probably won't get larger.
Overwintering alliums is tricky. If they are planted too early, or the winter has hot snaps, they can easily bolt (flower), and not make much of a bulb.
I'd think you should just go ahead and start eating them and try experimenting again this fall, maybe planting later than before.
Unfortunately the potato onions you have now, most likely won't be good to plant again. But you can always try.

We did have a very warm winter. Why won't they be good if I plant them again?

Your potato onions certainly can be planted again. Just like any multiplier (shallots, etc.) if you plant one bulb, you will get several bulbs at harvest. Plant those in the fall and you will have even more the next year.

Usually I plant mine around the same time as my garlic (late October/early November) and also harvest around the same time as the garlic (late July).

I am in 6a (Northern CT), or possibly with a micro climate of 5b (bottom of a hill). Last year I planted in the beginning of July - was that too early?

DVTO2;Potato onions are not supposed to flower. Flowering develops seeds at the expense of the bulb.Which usually means that the viability of the bulb is severely damaged. If they are true potato onions and grow as multipliers not seeders, I concur with crisis mode. The red flag is flowering.

Hmmm, maybe these were not potato onions then? I got them on ebay. Where can I find true potato onions?

Do you have a pic ?

I think beginning of July is probably way too early, and may be why they flowered. Any time after the autumn equinox is best. I planted mine along with the garlic in November. From what I've read potato onions are more frost sensitive than garlic, so I gave them a little more mulch. Mine were all harvested by mid-June this year.

Here is a link that might be useful: Growing guide from Southern Exposure Seed Exchange

These were planted in September. They multiplied but the bulbs were small, most no bigger than my thumb.

Just harvested mine yesterday. Planted in October, same time as Garlic. I finally figured out the secret to large bulbs. Plant them so that the tip of the bulb is just visible, then give them a good layer of mulch over the winter. The mulch has all decomposed away, and the clusters of bulbs were literally sitting on the soil surface. In spite of the early, hot, dry spring and summer, these are the largest I have ever gotten. Planted 6 bulbs, and harvested 30, every one the size of a golfball. Finally success, or they were on the short list for elimination!

Steve