Introducing a 4 Month Old Male Kitten to 2 Year Old Female Cat?

So I've had cats in my life,for about 20 years now, and I can say comfortably that I have a good understanding of their body language and signs of any sort of emotion. But admittedly, I've never taken the time to do formal introductions until now. Not because I just didn't want to, but out of my own ignorance to the whole situation. But this time, I've done a lot of homework and I wanted to do it right.

I adopted a female cat from a local shelter a little over a year ago and she has been alone ever since. I moved to a new place and decided it was time to get her a new friend, as I feel I just wasn't able to give her the play time she desired. Well, it's been about a week now and she was aching with curiosity when he came home and we put him in his separate room. She was constantly by the door, and eventually they began pawing at each other. At first she let out soft, not very serious hisses if he swiped too hard. Then she stopped this and joined in even more on the batting fun.

Well, they have been formally introduced and immediately they met nose to nose and began to chase around the house. If he got too playful on her face or pounces on her midsection, she lets out a little growl with her little hisses, nothing serious, and she never corners him or doesn't seem to actually want to hurt him. And every time he pounces on her and she growls and lets out a hiss, he darts off and she turns her back or chases after him to begin the play again.

Often she will just lie down and stare at him wide-eyed or pretend to be asleep. But she still will let out that little hiss and those little growls if he pounces at her. My question is, is this normal behavior or is she mad?

I understand that it could take some time for my older cat to really get used to him, but we're already at the point of them being in the same room and not messing with each other at all. In fact, she's asleep right now in her usual spot and he's curled up next to me asleep. But when it's play time, he loves to stalk her and pounce at her and she will do the hiss and growl. But she will more often than not come back and stalk him playfully or chase him about playfully. She loves to watch him, and seems to invite him to mess with her, only to let out those little hisses and growls if he gets too rough.

Should I just expect this behavior to go on for awhile? She is eating fine, not marking anything or destroying anything. She is her usual self with us and he seems very happy to have someone to interact with and is sweet as ever to us. I just want what's best for my two, and I'd hate to be stressing them out in any way. So when she seems like she's had enough, I make sure to put him back in his room. And when I do this, she will go and wait by the door, and curiously look under the door and even fall asleep right there! Any insight is appreciated. Just want to make sure I'm doing this right!

By Cory F from TX