I see your point.
Did some further testing, the global scope in each ISE tab is not shared.
Easily tested, create a global variable in one ISE tab, it is not visible in the other ISE tabs.
I agree with you that PowerCLI must be getting that connection info from somewhere else, and hence generate that error message.
Which imho is a bad practice.
I tend to consider this a PowerCLI bug, or at least not working as expected from the PS point of view.
Blog: lucd.info Twitter: @LucD22 Co-author PowerCLI Reference