When you purchase a game on the Xbox 360 Marketplace, you get two licenses for playing the game:
- The first one is connected to your gamertag (profile), and allows you to always play the games you buy, on any console, as long as you are signed into that gamertag.
- The second license is connected to the Xbox 360 console you purchased the game on, and allows everyone on that console to play the game, with any gamertag.
It sounds like you bought Assassin's Creed and Hitman Absolution on the console you and your brother are both playing on, but that you bought GTA V, Max Payne 3 and Tomb Raider on a different console. That would explain your scenario. (Source)
If that is the case, you can transfer your license from the other console to the one you're both playing on (you don't need the other console) by following these instructions.