When they accessed my account using the information they already had plus what they asked me for, they registered their device onto my account. They then got the OTP and related security warnings sent to their device. I then got the verification call on my phone, telling me to key in the code.
I think I'm the poster you referred to regarding the link. I don't do mobile banking because my phone is old and probably doesn't have up to date security so I only do online banking on my laptop so I asked my DH how it works. My hunch is that the scam goes like this;
You get a phone call claiming to be from your bank, asking you for your account number and sort code. The scammers may actually already have those details but by freely giving them you're marking yourself as someone gullible/vulnerable to fraud. Had you said 'fuck off you scammy knobhead' that would have been the end of it.
The scammers contact your bank with the account details (maybe over the phone, maybe you can do it online?) saying they can't remember the log in details. They can nominate any phone (maybe saying they've got a new phone number?) and get a OTP sent to it. But crucially the OTP must be put on the original phone registered to the account. Obviously, if this were genuine and not a scam you'd have both phones next to each other and it wouldn't be an issue.
But the scammer persuaded you to put the OTP into your phone which then allowed the scammer to access the account on the new phone, change settings, add new payees using the card readers etc.
I think the system is quite secure, but unfortunately because we don't know how all the systems work, we assume that if we can't see an obvious way for something to be a scam (eg the scammer giving YOU an OTP) we assume it isn't a scam. We need to stop being scared to just hang up at the slightest red flag.