Do I need to manually redeem Games with Gold titles, or are they automatically added to my library?

No, they won't be added automatically. You'll have to redeem them to add them to your account.

I'm not entirely certain as for the reason behind this, but I heard it's to avoid complaints if some people were to receive games they wouldn't want in their library.

However, you do not need access to your console to redeem the games. If you have a Windows 10 laptop, you can use the built-in Xbox Console Companion app (formerly "Xbox") to redeem the games without access to your Xbox. Simply access the Microsoft Store from within the app and redeem the games from there. Note: Do not use the Microsoft Store app directly, or else finding the games will be much harder.

Alternatively, you can redeem the games on any computer with internet access on: https://www.xbox.com/en-US/live/gold?xr=shellnav#gameswithgold

Simply select the game you want to redeem. The site should redirect you to the proper region, according to the account you're currently logged in as.