Am I wrong for not wanting my fiancée to talk to a guy she's attracted to?

A couple of weeks ago, my girlfriend met a coworker and told me that she feels something when he talks to her. I reassured her that crushes come and go; you meet all kinds of people in life, and sometimes you’ll feel chemistry with someone. I asked her what she’d do if she developed a crush while talking to him, and she said she would stay with me.

Recently, I found out she’s planning to hang out with him outside of work to study a common interest. She was upfront about her intention, and I know it’s innocent—she’s always been an honest and genuine person in the two years I’ve known her. But it’s really bothering me because spending time with him outside of work could easily lead to them growing closer.

I feel awful because I don’t want to hold her back from enjoying life, either. She’s very happy at home, and I do everything I can for her: I give her gifts, cook for her, and spend all my time off taking her out and trying new things. She doesn’t have many friends, though she tries to make them, and this guy has been giving her consistent attention.

Edit: I talked to her again about how upset I still was. She’s now cut off contact with him and won’t talk to him unless I’m comfortable with it. She also said she won’t hang out with anyone she feels chemistry with. Thanks to everyone for the thoughtful advice!