The Adjustment Date is the date of Sale. Owners you add will be billed the day after this adjustment date. For example, if you wish for the billing to be effective on the 1st of May, you will need to set the Adjustment Date to 30 April.
If you add a horse to an owner with a share, the horse will be saved in the owner's Horse Accessibility section.
If you add a horse to an owner with 0% share, the horse will be saved in the owner's Other Horses section.
If you want to move horses from the owner's Other Horses section to the Horse Accessibility section, you will need to repeat the above steps and apply a share for the owner.