Agreed. I have at least two or three tabs open at all times. I always open combat simulator in another window so I can transfer info over and reload and resend easily. I attack from a separate tab, and I probe from a separate tab. I have never been warned or banned. I don't know what sequence of events led to your being warned, there are likely still bugs in the auto-ban feature of the game, but tabbed browsing is nothing at all to be wary of in my experience.
Your original post referenced a concern that you were bashing. From the rules-
4. Bashing
It is not allowed to attack any given planet or moon owned by a player over 5 times in a single 24 hours period.
...
Note: Attacking fleets that are completely destroyed and Interplanetary missile attacks do not count towards the bashing rule. Moon destruction missions do count towards the bashing rules.
I have been accused of bashing numerous times, but the rules are quite specific. As long as you do not successfully attack a single planet or moon more than five times in a twenty four hour period, you are not bashing.
ETA: I do not doubt that there may be some sequence of events that leads to someone being erroneously warned or banned. But the fact is that there is no way for zorg empire to know whether or not you are using tabbed browsing, without excessive, unwarranted effort. I think the tabbed browsing thing is a red herring that should be disregarded if we are to isolate the true source of the problem.