Messages on iMac is pulling Apple ID conversations from iPhone

I have an admin account which is setup with my apple ID and I have another account with parental controls that is setup with my kids' icloud account.

Using Messages from the kids' user account, pulls up all chat history from my own iphone/phone number/apple id (whatever it is) when they send a message to a number in my contacts. So for example, if they send something to their dad by phone number, all of our convo is pulled up into Messages on their account. You can see how this might be a problem...?! They don't need to see those kinds of conversations between their parents... lol

Why is this happening? How can I stop it?

Thanks,

Sara

iMac with OSX Yosemite