Onions need some summer to develop fully. They let you know when they're ready because their foliage browns and dies down.

mushy is not a good sign.

typically i don't advise people outside my area as their conditions may be different enough from mine that my advice may not be appropriate. do you have greens? if not then you have problems. as the bulb grows and reaches maturity the greens die back. they go from bright green to dull and some leaves brown. that is the point where you withhold water, push the greens over gently with a rake to stop the plants growth. pull them in another week.

tom

The squishy part that you found on the onion bulb is the original bulb you planted. The new bulb grows on the inside and get nourishment from the mother bulb.