Tweens tend to be short, like a fade in, slide in, or affect some property. Are you apply a constant tween or a yoyo type of effect of some sort?
There's a million ways to do this, we just need to know what you want it to do. Code examples preferred.
It should be a constant tween e.g. a fade in of text, then a fade out of text. This will be used on banner ads. So not to complex tweening.
A couple things. I'll stick on topic to be easy at first and then make a recommendation.
First, Tweens are applied by you, when you want them to happen. Once you apply a tween and fire it off, at the end of that tween it will never happen again. Not until you tell it that it should and even then you will need to rebuild your tween. From what you say you suggest to me (and I can be wrong) that you think a tween is an event based class where when a movieclip has a tween applied it will be fired off every time that movieclip changes, or loads, etc. That's not true if that's the case. You must explicitly set up the environment for that to happen.
In the code you use to load the next SWF it is your responsibility to first manually tell the current SWF to tween out. Once that's done it's your responsibility to load in the new SWF. Once you detect it's loaded, it's your responsibility to re-apply the tween to fade it in. There is no automatic nature here. You tell it to tween, every time you want it to.
Second, consider using a light-weight Tween class such as http://www.greensock.com/tweenlite/ TweenLite. The are smaller in file size, much faster and very easy to use. They support extended features and are optimized well beyond the built-in tween class. Examples and demonstrations are provided on that site for the class. It's extremely easy to use and if you do feel free to post code or ask for help if you need it.