I was going to try to fool nature last year and started bulbils indoors in January and was going to refrigerate them for a month and then replant out during summer. But my experiment was not really successful, since the bulbils did not really grow bigger indoors even the they were growing green tops.
If yours are still growing, it may take so long time for them to be cured and rested for next season that it is already too late to plant for this summer. If those are planted to pots, I would move the pots outdoors and plant them in ground in the pot. That is how I have done for the bulbils, which I planted in end of February and kept in cool garage until ready to move to unheated greenhouse. When the soil in the raised beds had thawed I buried the pots in the soil. This way the bulbils are easy to lift and keep varieties separate. I can let the tops totally die and then dig up the pots and find the rounds in them. Depending on the size of the bulbils, I have planted multiple of them in same pot. Digging the pots into the garden keeps them better at proper moisture and temperature and the roots can also grow to the garden soil through the holes in the pot.
If the tops are still green, but floppy, I would not cut them before planting outdoors, since those green leaves are still photosynthesizing and letting the round grow bigger.
In any means I am not an expert in this area, so this is just pure speculation based on my limited experience with the matter.
Sari