The fact is you paid. It may be user error but they need to prove with these tickets that you had no intention to pay. They can't prove that because you did pay and have proof of such.
We had similar in Berkshire. Went out for lunch, put our details in to a parking app for the place. Three weeks later we got a £140 fine, which they said could be reduced to £70 if we paid within a set time.
DH was going to pay, I refused.
These replies to appeal on these cowboy websites are copy paste jobs because they expect the person to just pay to shut them up.
I still refused. I showed them via screen grab that it had been paid for, that the software had failed to log our vehicle currently, and when they kept threatening court action on the phone I said "OK please send us the date, I will advise you that I will be counter claiming because this will inconvenience myself and my husband due to childcare and work".
I then received an email saying they were "holding" the debt on file and could call it in in the next 7 years. It's been 6. Nothing since.
The fact they've admitted you paid means I think you'd have no problem winning an appeal.