my question is what is the process of withdrawal on most of the sites, which is so fast and without any double spending or issue like that?
Are you asking that from the developer side of things? As far as I know, most casinos use some form of payment provider that handles the actual transaction process.
Usually it's just a piece of software that can be remote-controlled to create a transaction and send it away, to the user.
But everyone knows that's not how fast withdrawals actually work, there's usually some other software running forensics on the account to make sure that it's not cheating, "mixing coins", doing arbitrage or any other shady stuff.