Remember that cat introductions are stressfull on the resident cat and
the new cat.  Sounds like you did things corrently.  The key to cat
introductions are slow and patience.  It's important that when you do
put the cats together that it's for just a little while.  Never touch
the cats while they are getting to know each other; this can lead to
jealously.  You should keep a spray water bottle on hand in case things
get out of control and never spray water directly in cats eyes.  Try in
do some activities that will be fun for both of them, they love the cat
dancer.  Cats are very good mood readers, so when they are together,
make sure that you are calm because they can pick stress and it will
make things worse.  Never get frustrated as it will take time and
patience.  When cats do meet for the first time they have to work out
the social order, so pouncing, hissing, slapping is all part of the
process and this behavor cannot be stopped or conditioned.  Eventually
they will learn to exist and how to tolerate each other.  The beavior
you are describing is perfectly normal, but remember it will take time.

PJC

It's hard to tell sometimes if they are playing or fighting.  I have two
neutered males and two spayed females.  Sometimes the two males will get
into it.  It sounds like they're killing each other, but they really are
just playing.  They also get into bad moods just like people do.  The
tabby male will sometimes pick on the tiny little spayed female, but 10
minutes later they will be grooming each other.  From your original post,
it does sound like the little one is playing.  If the older cat doesn't
cry out really loud, they are probably not really fighting.  If the
younger one doesn't release the older one when it cries, there's a
problem.  They will usually stop when one of them cries, especially when
they are first getting to know each other.

I'd pay lots of attention to the older one so the little one can see that
the older one is your baby.  Very often, a cat wants to know that you will
protect him/her from danger.  I know other posters said stay out of it,
but I think you need to step in when one of them seems in distress.  I
have an older female who's very afraid of one of the males sometimes.  But
she also has little swat fights over every single meal with him.  Cats are
complicated -- sometimes their spats are deceptive and are really play.

Wow, is that a long-winded and confusing answer, or what?

It's important that one cat doesn't get jealous of the other. If that happens
the fighting can get mean. That's one of the reasons it's important not to take
sides in their fights. (as long as they're not actually hurting each other)
They've got a lot of issues to settle. Important things like who can sleep where,
who eats first, etc. It's best to let them do that on their own.

If you handle it right the two will become the best of friends and you'll be
wondering how they ever got along without each other. Give them time and love
and they'll be the best of friends in no time.