I think you're worrying too much. You wouldn't be able to know what time people have their catches anyway since time is relative to when someone joins a comp. Competitions are asynchronous, only tournament semifinals and finals and custom comps have strict times.
In competitive fp what I would advise is running custom comps with the template (weather/time) of the comp you want to practice for and try to find ways to get scores you need, then it's just a matter of luck and repeating things over and over for the plan or rotation you've found and aim to get your practice score in actual comp too.
I've no idea really if incognito works on other platforms but I really don't see what kind of advantage it would give to someone, I personally just turned it on once out of curiosity.