I had not. However, that seems specific to customizing new ISE basic tabs as "Remote tabs" using Remote PSSessions and avoid loading the PS_ISE profile or not. I don't see anything in there that applies to what I'm seeing with the Connect-VIServer or that speaks to global variables - likely because it doesn't appear that the PSSessions use global variables the way PowerCLI uses the global:defaultviserver(s).
I'm currently trying to figure out what - if anything - Connect-VIServer in my current tab changes in the global:defaultviserver(s) variables in another tab. It's a stretch, but we'll see.
But this isn't something strange with my setup right? Others have the same issue?