When you get into the details, each situation is so unique that comparing them on such a high level as this isn't useful.
In the cases I'm aware of, there have been additional circumstances (big and small) that contributed to being pursued. It's rarely down to "Person A spent three months in France, three months in Australia, six months in Dubai, and a couple of days in transit." Those things can and do matter. But it also matters what they do during those three months, what connections they establish, how the business operates, who is involved in the company, good/services sold, and so on and so forth. It also matters where you're spending time. Some jurisdictions are more gung-ho than others about dishing out tax residence at unsuspecting foreigners.
As an example, someone might've gone for a setup very similar to what you're proposing. But they have kids and found a daycare that caters to expats, and so they sent their kids there for three–four months. In some jurisdictions, that's enough for the tax authority to potentially look into you.
In another example, someone met, liked, and hired a local person to join their business as a contractor. Should you pay social security contributions? Did you perform a meaningful business transaction locally within the local economy? Does your business have a significant presence there now and be liable for tax going forward?
Then we have the people who post on social media flaunting their wealth in the wrong place at the wrong time. Not exactly enough to make you tax resident, but it can draw attention.
Medical procedures, property ownership, property rentals, unexpected police involvement, and other things that are more or less predictable can also matter.
So even though you have your structure in common with these people, the real life scenario plays out differently.
Also worth keeping in mind that just because the tax authority claims something and tries to come after you, doesn't mean they are right and would win if you actually fought them. But it's a lot of work to fight a tax authority.
And for everyone that's caught, there are usually many who aren't caught — either because they did nothing wrong or because they simply slipped through the cracks.
Be aware of and manage your risks. Seek legal advice for the relevant jurisdictions. In your case, I'd say it's very unlikely you'll get caught (and less likely you'll actually be tax resident) if you don't get too involved in the society.
