Regarding this particular Red's world
First off, I'd just like to say this is an AU!Pokemon Special. Secondly, I'd just like to say that this may be a rather messed up AU.
In it, the first seven Pokedex holders and Emerald serve Team Rocket. Ruby and Sapphire respectively served Team Magma and Team Aqua, though since Maxie and Archie's disappearance, are currently unaffiliated with any evil organization.
Regarding characters that were in Team Rocket in the canon universe, they still are in Team Rocket. This means Giovanni's still boss, and Koga, Sabrina, and Lt. Surge are also members themselves. And, like in the canon, Blaine quit being a scientist for Team Rocket.
Now, everything has its beginnings. In Red's case, his mother is a member herself, so she managed to get him to join. With Green, his grandfather works for them, but this is currently unknown to the public. Green's affiliation is also unknown. Blue's doing it to make sure they won't do anything bad to Silver, who was caught when they planned their escape. With Yellow, let's just say her personality is the opposite of her canon personality. Gold has a similar case to Red, his mother and father being members. Crystal, like Green, has an unknown affiliated, being Professor Oak's assistant. Emerald's there because Crystal's there.
In what would be the RGB arc, Team Rocket maintains its control of the Kanto region. Red and Blue both "steal" Pokedexes and Pokemon from Professor Oak, as the public hears it. Red also manages to steal four of the eight Kanto badges, the rest being given to him by the Team Rocket gym leaders. As for the tournament at the end of the arc, Red, Green, Blue and Oak all enter, and Red still comes out victorious, to the public's dismay.
The Yellow arc has basically the same plot, with Pika being captured, Red disappearing, and Yellow being trained as a Rocket Grunt. Everyone takes on the E4, they beat them, etc.
Now we reach GSC. Gold, Silver, and Crystal got their Pokedexes and Pokemon the same way the public heard Red and Blue getting theirs, except the three actually had to steal their Pokedexes and Pokemon from Elm. Gold and Silver stole from Elm while he was in the lab, but Crystal waited until he was at home before she went and stole the remaining Poke Ball. At some point, Gold, Silver, and Crystal all attempted to capture the three beasts they had worked with in the canon, but all failed. When the tournament came around, everyone led a surprise attack, helping Pryce come out victorious. As a result, Team Rocket also managed to continue controlling the Johto region.
I would go into detail about the RS arc, but because Red isn't in it, I'll skip to FRLG. This is basically the same five Pokedex holders in the canon arc attempting to capture Deoxys and Mew. Red is pulled just before he and his comrades are turned to stone.
In it, the first seven Pokedex holders and Emerald serve Team Rocket. Ruby and Sapphire respectively served Team Magma and Team Aqua, though since Maxie and Archie's disappearance, are currently unaffiliated with any evil organization.
Regarding characters that were in Team Rocket in the canon universe, they still are in Team Rocket. This means Giovanni's still boss, and Koga, Sabrina, and Lt. Surge are also members themselves. And, like in the canon, Blaine quit being a scientist for Team Rocket.
Now, everything has its beginnings. In Red's case, his mother is a member herself, so she managed to get him to join. With Green, his grandfather works for them, but this is currently unknown to the public. Green's affiliation is also unknown. Blue's doing it to make sure they won't do anything bad to Silver, who was caught when they planned their escape. With Yellow, let's just say her personality is the opposite of her canon personality. Gold has a similar case to Red, his mother and father being members. Crystal, like Green, has an unknown affiliated, being Professor Oak's assistant. Emerald's there because Crystal's there.
In what would be the RGB arc, Team Rocket maintains its control of the Kanto region. Red and Blue both "steal" Pokedexes and Pokemon from Professor Oak, as the public hears it. Red also manages to steal four of the eight Kanto badges, the rest being given to him by the Team Rocket gym leaders. As for the tournament at the end of the arc, Red, Green, Blue and Oak all enter, and Red still comes out victorious, to the public's dismay.
The Yellow arc has basically the same plot, with Pika being captured, Red disappearing, and Yellow being trained as a Rocket Grunt. Everyone takes on the E4, they beat them, etc.
Now we reach GSC. Gold, Silver, and Crystal got their Pokedexes and Pokemon the same way the public heard Red and Blue getting theirs, except the three actually had to steal their Pokedexes and Pokemon from Elm. Gold and Silver stole from Elm while he was in the lab, but Crystal waited until he was at home before she went and stole the remaining Poke Ball. At some point, Gold, Silver, and Crystal all attempted to capture the three beasts they had worked with in the canon, but all failed. When the tournament came around, everyone led a surprise attack, helping Pryce come out victorious. As a result, Team Rocket also managed to continue controlling the Johto region.
I would go into detail about the RS arc, but because Red isn't in it, I'll skip to FRLG. This is basically the same five Pokedex holders in the canon arc attempting to capture Deoxys and Mew. Red is pulled just before he and his comrades are turned to stone.