No, its more about how you post those links. If you're posting the same tweets on loads of accounts all at the same time then they will pick that up pretty quickly, you have to mix it up as much as you can. I have hundreds of accounts posting links to the same website everyday without any problems.
No I spin all the tweets as much as I can. Sometimes writing two or three tweets for the same link and spinning them together as well.Do you post the exact same tweets on all of them, but just set up different times of posting? That shouldn't be too hard to do.