We have a variation of this system here (India)
During checkout you can select netbanking as payment method. It asks you to select your bank and after you select it and click next/pay, it redirects you that bank’s login. You login, provide OTP, and it redirects back to the website you were shopping at, usually to orders page.
As far as I know, fake version of bank’s website will not work because the redirection happens from payment gateway with hardcoded linking to bank websites.