So this is my theory :
In Super Watermelon Island, Lapis and Jasper are washed up on shore. They're both passed out but Jasper wakes up first. Jasper sees the Crystal Gems around her and gets scared after all the stuff she went through. She runs away.
In Gem Hunt, Lapis, Steven, and the Crystal Gems go on a gem hunt to find Jasper. They find a scared Jasper hiding. They poof her and Steven feels bad.
In Bubbled, Steven goes in the Burning Room after 2-3 episodes to find Jasper. He frees her from being bubbled. Steven and Jasper bond over time. The Crystal Gems try to poof Jasper once more but Steven stops them.
In the Kindergarten Kid, Jasper makes fun Amethyst and compares herself to Amethyst. Upset, Amethyst attacks Jasper and declares a short war. The two fight but make up in the end. Also, it reveals Jasper was born there too.
In Know your Fusion, Garnet teaches Jasper about who she is and why she wants to be fused forever.
In a later episode, Pearl and Jasper fued because of Pearl's origins.
In Alone at Sea, Lapis and Jasper bond and make-up.
In Same Old World, After bonding with the gems, Jasper still wants to go home and still thinks Homeworld is good. Peridot believes that they should tell her the truth about homeworld, and why she betrayed homeworld. The Crystal Gems do tell her.
In Hit The Diamond, Jasper finds the communicator. After talking a little bit with Yellow Diamond, she is disgusted and realizes how bad she is. Which leads to her to betray homeworld.
I know Peridot's redemption took like 8-9 episodes, but Jasper's WILL take about 10-11 episodes at least.