This is incorrect and not how paypal handles refunds.
This is merchant 101: always refund suspicious payments before your payment processor has to do it, it'd be really bizarre if Paypal was somehow the only exception in the industry.
FDSGSG is absolutely correct. He should have immediately processed a refund on the $600 as soon as he saw the transaction. By not doing so he risked getting a chargeback and loosing not only the $600 but an additional $10 PayPal chargeback fee.
There is no risk of OP loosing $1,200 to two refunds if he went through the proper refund procedure. A transfer can only ever be refunded once.
The only way I see this going wrong is if instead of doing a refund you create a new transfer to send the money back, but you obviously shouldn't do that.
