Right, you must report the repayment relative to the type of account the distribution came from, not the type of account to which the repayment deposit was made.
When the repayment deposit is made to an IRA, you are required to inform the IRA custodian of the nature of the repayment so that they can code it appropriately on the Form 5498 that they will provide to you and to the IRS. No other proof is necessary unless the IRS questions the repayment, in which case you would provide a transaction statement showing the amount and that the repayment was made no more that 3 years after the date of the distribution.
