What is the right way to deal with a jealous woman?

I wondered if it wasn't something like that. That's a tough scenario - you know women can be a little unpredictable. Maybe this other gal will take everything your ex says as gospel, or maybe she'll reject it outright. Also, it can give the appearance that you're working your way around the company (not saying you are, but if I were a vengeful ex, I'd throw that out there to see if it stuck).
I would be straightforward with the new girl. Make sure she knows you were dating the ex and that you two have parted, that you want to keep things civil between you and your ex, but that there was a reason why it didn't work out so you aren't exactly organizing each other's fan club. From there I would say go forward as normal, but with a sort of open door policy for questions she might have about this past relationship.
Or don't sweat it. People's characteristics are often similar in different environments. And it's hard to look good while trying to talk bad about someone (except when we were like 12 and then it was cool?), so with those factors out there, new gal might just think Fatal Attraction is being a bitter bitty. I dated a girl at my last place of employment. She turned out to be a head-case, but the only genuine problems I encountered with her friends (that related to her) were ones in my head, creating a problem by worrying about it.
You raise a good question. I say be open about it with the new girl, be ready to do some spin control, and be optimistic.

Move to Tennessee.
Depends on why they would be in contact. If your new gal is from the same circle of friends as your ex, then I don't like your chances. But otherwise it depends on what she's up to. Is your ex doing something specific?