Is it normal to be jealous and possessive until she is my gf?

This happens to me so much. When me and a girl I really like are dating/talking I get jealous of her associating or talking to other guys, even her guy friends. But as soon as we are exclusive or officially together, all my possessiveness goes away and I become much more secure and comfortable, and very trusting too.

Right now it's happening again. I really like this girl. And she definitely likes me too. Nothing's official yet we've just been talking. We hung out a bit when classes were on. I'm back home from uni for the summer and she is back to her parents home too. For 2 weeks she has had the entire house to herself all alone. She is still recovering from depression and has a very bad habit to isolate herself and not talk or meet anyone. I know this so I often encourage her to socialize. When I asked her if she did anything or talked to anyone she said she met a couple of new people and had a few calls. I lied to her that I was proud of her and that was progress compared to her old self, and encouraged her, but deep inside I was incredibly jealous. IIN?