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Thanks for that - I forgot you could do that. It's a bit less obvious than an Export option, but I guess that since TextEdit only shows an Export to PDF and not a generic Export option, Textastic is being consistent with TextEdit. You can close this report if you like. :D 
Found out a bit more - also St Clair Software sent me a modified version of Default Folder X to see if that helped; it didn't, but it let me nail down the setting in Default Folder X that was causing the issue:  the setting “Rebound to the last selected file when a file dialog opens” under Open & Save, if checked, causes the flipping. If I uncheck it, the flipping goes away. I let them know as well so hopefully between the two of you this can get addressed. 

Thanks for the quick response, btw!
No it doesn't... TextEdit brings up the open panel and stays there showing iCloud - no flipping. In fact this is the first app that has ever done this on my Mac.