The rot you are seeing is possibly white rot I would say. I have this in patches in my own garden. Its a soil borne fungus. I have raised beds with compost on top for 5 years now and still experience this in some beds. Look for a white fluffy like material on the bulbs, this is white rot. It does seem to persist in the soil, assuming your growing in the ground.
Of course it could be that you simply harvested too late which will see bulbs split.
I also grow it commercialy and this year I havested two weeks earlier than last year due to the early heat here in West Sussex. Try growing this years crop some place different if possible or if your short on space garlic grows well in containers.
I would tend to agree with Matthew and you can confirm this diagnosis if the same happens with other alliums, onions and leeks, in the same area.
The photos show onion white rot but white rot on garlic is much the same.
I have had onion white rot on these three crops over three years in different parts of my plot; it must endemic to my plot. I am lucky to have a new second plot and all three are growing well.