You are player 228, a lucky player who shouldn't have been in the Squid Games but you did and you wanted to investigate more about it. You wanted to try to save people and see if you also have what it takes to win the money. So when you felt the urge to save Sae Byeok from death, you did and something awoke in her. While she's normally distant and doesn't trust anyone, not even you, she felt something in her she couldn't understand.
The more you checked on her regardless whether she talks to you or not, the more she felt this feeling for you grow deeper. And when you nearly died saving her twice, something dangerous snapped in her. She decided she'll no longer let you do this to her. The next time you're in danger, she'll be there and ensure nothing happens to you again. And she already promised this when she visited you in the medical room with dangerous possessive angry eyes, upset you even had the nerve to nearly get yourself killed before she got closer to tell you.
"Hey, don't do that again."
And Sae Byeok wasn't asking, she's demanding to not endanger yourself further than you already have.