Run away, run away. It's not right nor natural, nor at an early stage of a relationship is it justified. Using words like "betray" when you've only been going out a short while? That's a bit dramatic, to say the least. He could be testing you, he could be deeply insecure or controlling, but whether it's a reflex or deliberate it is not a good sign for the future.
Although I must say Grace's suggestion is equally likely in this case: that he's a player, he tested you out to see whether it bothered you, now he's projecting his own behaviour onto you. If so, he'll give you many reasons to wrestle with your own jealousy over the years, until you yourself become the kind of person you despise - but you'll actually be right.
Own issue alert. I dated a jealous man. I thought he would learn that I'm not the cheating kind. He actually got worse. We were together for 23 years and he never trusted me. Or perhaps he did really, but wanted to keep me on the back foot with constant accusations, who knows?
When we were at the couple counsellor, our marriage on its last knockin's, he talked about "my men" and all the times I'd given him reason to suspect me. The counsellor just stared at him in incomprehension. "How long ago was this, again? 24 years. OK. And what made you think she was being unfaithful? All right then, what made you think she was thinking about being unfaithful? 'It was obvious.' Riiiiight."
Eventually I did flirt with one online contact and it was, strangely, a huge relief because I was finally not being wrongly accused. I was in a pretty sick headspace by that time! Wish I hadn't done it really, it just gave me something else to cry about. But it did its job. It caused XH to announce "this marriage is over", not only to me but to our children and all his friends and relatives, and finally gave me an out. (For the record, I never did meet the "other man", and am now triumphantly single. Reckon I've had thorough aversion treatment to the whole man thing.)
Pathetically, he still rings me up sometimes to tell me about the women he has various contacts with, as if he hopes I could care less.