No, You had no need to refund.
All you need do was refund any expedited shipping that the buyer had paid.
Now your option is to send the buyer a pre paid return label and request return of your goods.

You shouldn’t have refunded.

There were two legitimate options.

1. The customer was unhappy that the item was delivered late but had paid for expedited delivery. You would need to refund the delivery charge.

2. The customer no longer wanted the item as it was too late for the intended purpose. You should have accepted a return and waited for the item to be returned to you. Only when the item was returned would you need to issue a refund.

Was it one of the ‘We’ve been contacted by one of our mutual customers regarding an order placed with you.’ emails that said you had to refund?

Amazon Customer Service Department tend to have zero understanding of policies and make unreasonable demands on Sellers over what you should do for the customer which should normally be ignored when replying to the customer.

First they tell me to refund without having the item back and now after many complains they say that I should not have refunded without having the item back.
I have sent them the email where they ask to " refund and don’t wait " and their answer is:

we don’t have anything to add and we close the case. Be careful you did not respect Amazon’s terms of sales.

So it is all my fault ! I have refunded the item, I don’t have the item and I may have a penalty because I did refund.

BTW buyer changed mind and would like to keep the item. I told him he can ask Amazon to be charged for the item and his answer was " we will see about this "

I guess I am just an idiot that I sell here, follow their instructions in the mails and give items for free.

I have closed all listings. I have asked Amazon UK to escalate this to a higher level and make things clear. I just did what they told me to do, nothing else.

Hello Sofias_Bijoux1

For clarification, when it comes to refunding buyers, there are policies that protect the seller, and also protect the Handmade seller for personalised products.

Please see the following which details your rights under our Handmade policy

Handmade Returns, Refunds and Cancellations Policy

It may help to know that whenever in doubt on what actions to take on your Handmade Seller Central, and especially in relation to Handmade buyer issues, please feel free to contact Handmade Seller Support.
While there are many departments in Seller Support that can advise on the Seller Central issues, it is by raising a case for Handmade Seller Support where you can get direct and clear advise in in relation to the Handmade side of your seller central.
You can raise a case directly with Handmade Seller Support via your seller central > help > contact us > Selling On Handmade