Girlfriend is Very Close with Her Male Coworker

My gf and I live together. We get along very well, both satisfied with the relationship. My gf is in an internship and has 2 coworkers, 1 guy 1 girl. I recently found out She’s texting with the guy. He texts her “good morning 😊 (or 🫠)” before work sometimes, sends her music to listen to as well. They “heart” each others messages on iMessage. My gf has sent him music as well. They also talk about a tv show my gf and I are currently watching. She said they’re just friends, he has a gf etc. I told her this is inappropriate, and I trust her not to hide anything from me now that I have set the boundaries. Her response was reasonable, fair and didn’t raise any further suspicions. So, how do I make sure that this sort of stuff gets shut down in the future?