To the best of my knowledge, u can't download games u installed via non-legit CIA from the eShop. Pretty sure u need the games ticket installed to do that. You can get tickets with homebrew such as freeshop or CIAngel.
If u wanna update a CIA that is the correct region for your console, just enable internet on your home screen, highlight the game, and wait for it to tell you that an update is available. Press A and a menu will open, then press Y to update.
If u are using an out of region CIA, I believe you must also get the updates for that game in CIA form and install them that way.