But there is no real reason for UK to actively track residents and tell them "you know what, we discovered that you should pay your money to another country, not us". What is more reasonable is that the third country would symay "hey buddy maybe you should be paying your taxes here not in UK" but in this case Barbados said they wouldn't
Yep, most people get this rule the wrong way around. The 183 day rule is a sufficient (but not necessary) condition to be considered tax resident in most countries. It does not automatically make you non resident in your home country and if you don't actively communicate to your home country that you moved abroad it all comes down to the existing double taxation agreement between the two countries.
