No, you're not supposed to cut the greens. You didn't mention if the tops were falling or not, usually this is the indicator they're ready. If you're pulling them too early, that could be the problem. Otherwise, the shade you have them in may not be drying them quick enough, plus the dew might be rehydrating them each night.
I put them on the wooden floor in my barn with a fan on them. Some sunlight is good, but hot California sunshine will probably cause them to sunburn, so be careful.

Warm, dry and good airflow should cure them down within 2 weeks or so.

Good luck,
Mark

Thanks..

Yea the tops were falling over and starting to brown. You may be right about the dew... I'm somewhat close to the ocean, about 8 miles.. So warm and dry?

So what causes them to sprout? I may have been confused about the warm part, or do you move them to a cool place after curing?

Definitely warm and dry! (At least for the cure.)

When I was young my parents harvested the onions when the tops were all down and dry. Then the bulbs went in the empty north side of the corn crib to cure under a roof, dry, well ventilated, and occasionally hot (NW Iowa prairie). Same for potatoes.

I use old window screens in a partially opened west facing screen porch. Dry and airy, also occasionally hot. Works for tulips, garlics, onions, both bulb and multipliers and potatoes. It gets a little too chilly by the time sweet potatoes are ready; so they get cured in the kitchen.

The difference is when the various types are ready to harvest. For onions, unless to use immediately, the tops need to be down and dry before you pull the bulbs. For tulips and garlic that is far too mature; them you dig at least somewhat green and leave the tops attached. But for all of them once out of the ground dry is the key, even if you have to cover them against dew. One of the nice things about the old corn crib, was that dew didn't get inside the ventilated bins. It doesn't get into my screen porch either.

Wow! Lots of good info... I had them curing on the north side of the house in a soda crate with a bunch of 1/4 " holes but uncovered. Hmmm Maybe I'll keep them on the south side next to my garden, covered up with a secure paper bag. It's warmer there. Not sure if I'll still have a problem with the dew getting in, covered with the bag... The dew can still get in through the crate holes... I'll try it and see what happens...