Your wallet will continuously backup, even if you never open Exodus. This is because your funds live on the blockchain and Exodus is a blockchain interface that reflects the data found there.
When you restore your wallet from the 12 words, FEX overwrites any previously existing FEX wallet on your system and re-generates the private keys for the wallet using those 12 words as the seed. Because the secret 12-word phrase is not connected to any password, that means that after restoring, there is no password protection on your wallet. It must be re-enabled by setting up a new one in the Backup menu. After restoring from your secret 12-word phrase, the first thing your should do is protect your wallet with a password.
Leaving your wallet unencrypted leaves you open to easy theft, so it is important you go through the backup process again. Remember to set a unique password, that you don’t use in other services. Re-using passwords opens you up to the risk of theft.