Tina was a relative of Carrie
They both have mental powers, they both are messed up, and the book did say the gene for telekinesis only expressed itself in females.- The movie as a whole is a lot more entertaining if we just pretend it is Carrie.
Jason took mercy on Tina
Jason knew Tina was responsible for reviving him, and as a small bit of gratitude he didn't kill her right away. He jammed the metal spike in her cabin doorway as a warning that she needed to leave his territory. This is why he goes out killing nearby campers in the woods first.