I had a different issue...
The key shows up fine on my profile, but after redeeming it on their page, the DLC did not show up on my profile at TE4. Since the GOG version works terrible on my mac, I depend on playing the standalone but for that I need the redeeming key to work...
Now the website tells me the key is already redeemed, but I can't download the DLC.
I don't know if this should be published here or if I should send a message through their page, so I'm doing both and will wait to see if one of the sides can help me.
You don't get the DLC directly when you redeem the key at the TE4 website, instead you get enough coins that you can purchace the DLC.
If you click on DLC in the menu you should have enough coins to buy the DLC on the TE4 page.