Personally, cute is the last thing I called displays of jealousy. Best I can do is a knowledge it as a character trait. Some guy on the radio said he liked making his girlfriend jealous. -_- don't wanna say what that made me feel like doing to him. idk. I seem to be at odds with the comment sections here half the time anyway.
Intentionally making your significant other jealous is, I would say, pretty different from someone being jealous that a little kid is being friendly with the person they like. That boyfriend sounds like a shit, I totally agree. In this case, however, it's really just a childish reaction to something innocuous.
Regardless, I'd say Adachi was mostly just annoyed that a strange little girl suddenly inserted herself into the plans she had to spend a day alone with Shimamura. Frankly I don't think Shimamura was particularly enthusiastic about it herself. She wanted Adachi to stay, and asked to make sure Adachi wasn't going to run away a few times. I guess she might have just wanted to not be left alone with the little girl, but I don't think that's likely.