On site is for wholesaler and every product has a different "Minimum Qty Allowed in Shopping Cart" set as well as a "Qty Increments" set to match. Meaning it might be added in lots of 6, 2 or any number. They all differ.
The second (and new) site that's been added on the same install is for retail and both of these figures need to always be 1.
When the option is updated at a store/site level in Magento admin is overrides the other. It looks like you can't set these options on a site level.