Knowledge can affect jealousy in two ways (probably more, but two that I can think of).
One: finding out that things aren't as bad as your worst imagination made them out to be is reassuring. They had sex, and she still came back to you, she still loves you, the world didn't end. That's the good way.
Two: finding out fuels your insecurity, makes you hate the arrangement, and shut down or want to end the poly aspect. That's the bad way.
I'm a very open person. I talk about my husband sometimes on dates, not like... in your face or making a big deal of it... just in the sense that we share a life together and there are parts of me that are related to him and affect my behaviour. This seems to feel more comfortable when the person I'm on a date with is also in a serious relationship. I find myself doing it less when I'm on a date with a single person.
I also tell my husband about my dates. He's my best friend, and you always tell your best friend when you have an awesome date! It hasn't happened yet, but if I get intimate with someone, I'm definitely going to tell him that it happened, but I don't intend to give him all the "kiss & tell" details. As far as I'm concerned, that's between me and the other person, and I respect his or her privacy.
Gralson: my husband (works out of town).
Auto: my girlfriend (lives with her husband Zoffee).
The most dangerous phrase in the English language is "we've always done it this way."