St John Paul II did have a tiara on his coat of arms; so putting the image of one on a medal is not really proof of anything.
There is no way of knowing if the medal was minted first, then someone decided to make a tiara to look like the one on the medal.
Do we even know if the medal is authentic?
As for the tiara itself I would ask “who” made its existence known?
I mean, I could have knitted him a scarf in 1988, never gave it to him, then one day say “this is the pope’s scarf, I just never had a change to give it to him.” It wouldn’t mean much.
If such a thing exists, it would be either in a Vatican museum or given to his relatives upon his death as personal property. If the Vatican has it, why keep it a secret? We know he never wore one in public, so what purpose would it serve to keep it hidden?
As for Benedict XVI
We know that one exists. No doubt. Plenty of pictures and plenty of reliable first-hand information.
Still, is it really accurate to say that it was the tiara of Pope Benedict if the Pontiff himself never wore it? He did not commission it. He did not request it. Some people simply surprised him with a gift. I don’t think it’s fair to call it Benedict’s tiara under the circumstances.