I think it is a good idea to upgrade and test again. I am running different versions and it is working nicely. Opening different browser tabs (Chrome) and they are working without impacting others.
Node-RED : 2.1.0 - beta.2
Dashboard: 3.0.4
Windows 10 - Chrome
PS: After upgrading the dashboard to the latest version I could reproduce the issue you mentioned. I did a testing by opening three browser tabs.
So, my conclusion is that the ui_control node behaves differently from dashboard version 3.0.4 to version 3.1.0.
Version 3.0.4
The ui_control node will receive three messages from the function node but will output only one to the connected debug node (updating only one browser tab).
Version 3.1.0
The ui_control node receives three messages from the function node and output three messages (one for each browser session opened).
I was expecting a behaviour like explained in below post: