Worried he still has feelings for his ex?

I’ve started seeing a guy who I’ve known for a long time (10+ years). We had coffee for our first date yesterday afternoon and then we went back to his place to watch a movie. All we’ve done so far is hug and kiss. Not got as far as making out yet.

He left his Facebook open as he was in the kitchen making coffee, and a message popped up from his ex girlfriend. They had been together 3 years and he ended the relationship, as he didn’t have romantic feelings for her anymore. They broke up about 6 weeks ago… I know that’s quite recent, but the fact he did the breaking up and lost romantic feelings made me presume he was over it.

I wasn’t intending to snoop, the idea of doing such a thing horrifies me, but my curiosity got the better of me and I started scrolling up. The conversations were REALLY long, there was nothing sexual, flirty or romantic in them, but they were being very friendly. In fact I’d say she was the one being more friendly – she was using a ton of emoticons, he wasn’t.

However, he was the one who initiated all the conversations… The last week they have spoken every day and he initiated every single one of them. I don’t understand why he would do that if he broke up with her because he’d be giving her false hope, wouldn’t he? Especially since he told me she was very upset when he broke up with her and she struggled with his decision a lot.

Although I’m glad there wasn’t anything romantic in the conversations, at one point he did tell her she was an amazing and wonderful person, and he was thanking her multiple times for her ‘kind words’. She even asked him for coffee and he responded saying that it would be nice.

I’m a bit concerned to be honest and wondering whether I should continue seeing him… What do you guys think? Do you think he might still have feelings for her?