It's hard to say because it could be your instinct telling you something is wrong.
However I had a near identical experience with a male colleague abroad once. The reality was it was very boring and lonely. We met up on the weekends, went to museums, had meals and talked. We talked about mutual colleagues, our jobs, what we did previously, where we grew up, why I was single, the type of guy I would like to meet, his friends at home, how he met his girlfriend, how their relationship evolved and what his plans for the future were.
I enjoyed spending time with him as the conversation flowed so easily and he was a really nice guy. It's also nice to spend time with a new person to get different perspectives on things. At no point did he give any indication he had any romantic interest in me whatsoever. In fact I would have no idea if he would have considered me objectively attractive in a 'if I was single' way. That dynamic to our interactions just did not exist. When we got back we didn't stay in touch or have a closer working relationship or anything like that. We were simply passing time together.
I also did go shopping with him one day - he was mainly on the phone to his girlfriend and I remember him laughing down the phone to her at how I was the fastest shopper he'd ever seen - he basically stepped outside to take the phonecall and I appeared with the shopping bags shortly afterwards. So the visuals you have of her trying on coats and standing in front of him waiting for am opinion might be complete fiction.
Now this was just my experience and I probably remember it in more detail than it deserves but the reason for that is I did sometimes wonder if it would give his girlfriend cause for concern. I realised how it might look (we were there for a few months) and I wondered how I would feel at home (probably as you do now) but there really was nothing whatsoever to worry about. Also, this might be irrelevant but I am extremely photogenic and if she had looked me up out of curiosity she would have seen an unrealistic representation of me.
Now that is just my experience and I can't say it's the same in your partner's situation but I wanted to point out that sometimes it is completely innocent.
Have they remained friends? Does he have mentionitis? Is he behaving differently?