I'll explain a little better. You are
I'll explain in some more detail. You may be a tax resident under domestic tax laws, but not a tax resident for purposes of the application of the tax treaty because you are only subject to tax from local sources. For example, in the UK - Cyprus tax treaty, this is in article 4 (the residence clause), paragraph 1: "This term, however, does not include any person who is liable to tax in that State in respect only of income or capital gains from sources in that State."
What this means is that you are not protected by the tax treaty, because you are not considered a resident of Cyprus for purposes of the tax treaty. No protection means that other countries can claim residency under their domestic tax laws and levy tax on your income, despite Cyprus considering you a tax resident under domestic law. Now, that does not mean that if you stay in Cyprus the whole year that the other country will levy tax. You will still need to be considered a tax resident under the domestic laws of that particular country, which is typically not the case if you're not there the entire year. But, if you're there 5 months per year, and 2 months in Cyprus, then depending on the criteria for residency in the domestic law, you could very well be considered a tax resident. The tax treaty won't help you then.
In other words, all these structures relying on only 2 months in Cyprus are worth nothing, legally at least.
And all these structures that have a non-Cyprus
tax haven company (or a transparent LLC) paying
dividends to a non-dom Cyprus tax resident do not work either. Cyprus will consider these companies tax residents of Cyprus and tax them, because their management (you) is in Cyprus. Get a proper tax advisor folks; don't structure in a certain way because you read about it on a board.