If you navigate away from the new open window other than to go to the wallet provider and choose the wallet you linked, you won’t be able to sign the transaction. You’ll need to go back to civic.me and start the process again.
If you’re using a mobile device, you won’t be able to link a Public wallet. The workaround is to use a desktop and sync the changes. When you load your profile on your mobile device, you will then be able to view your Public wallets.