I‘m afraid they should have been planted or set overwater last year in October and kept cold since then. I don’t know how well they’ll succeed now since they’ve started to shoot but have no roots to sustain them. Sadly, it’s not unlikely that the flowers will abort or have already done so within the bulbs. I think your best bet would be to pot them up immediately and continue to keep them cool for a few more weeks in the hope they'll produce enough roots to flower properly. Here are some of mine from November in a previous year. Note the huge amount of roots they already have compared with the size of the shoot.

After 17 days they have some roots. I put a third in a pot with potting soil.

Temps cold but above freezing. Should I keep it cold?

They should have been kept both cold and dark to promote root growth. I realise I didn’t mention that. From the green shoots I’m guessing they’ve not been kept dark? However they look better than I feared. I’d give then another week or two to try and get more roots. The shoots look plump so I think you will get flowers but you will need to wait until they open to know if the buds have survived inside the bulbs.

Floral, would it have worked to keep them in water in a refrigerator over the winter? Do you keep changing the water?

I keep my hyacinths in their water glasses in the shed. I don’t change the water or put them in the fridge. The shed will rarely go below freezing. I only once remember a glass shattering when the water froze. They’re in the dark and cold and algae don’t seem to grow. The photo shows them as they are in the shed but uncovered. I checked and the picture was taken in November. I usually start bringing them into the house after Christmas.

They got indirect light in my garage, which has South windows, so they got light. I put a bucket on top of the bulbs tonight to block the light, if it is not too late.

All just an experiment for fun, to see what I can get.

Good luck. Let us know how they turn out. Crossing my fingers that the blooms haven't suffered from the late start.

After 36 days in water. Going to put in a sunny spot.

Well done. How are you stopping them falling over? When the flowers fade I just plant the bulbs out in the garden. Don’t wait for the leaves to die back, just stick the whole thing in the ground as it is.