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?
It depends on the site. Some take slightly long, while others take 1–3 minutes to broadcast the transaction. For example, when I am sending funds from exchanges like Binance, MEXC, Phemex. The transaction gets approved very fast as soon as i am done with approving the 2FA and email confirmation.
I had a very good experience with bustadice too sometime back. There were no delays when you choose the instant withdrawal option.