CY Law, Visas, Taxes, Insurance
Your non-EU family member does not need a visa if they have a residence card.
With this residence card (or permanent residence card) they can travel visa-free to all EU countries (including the country of your nationality) as well as to Iceland, Liechtenstein and Norway, also without being accompanied by you. This applies regardless of which EU country issued their residence card and the country they are visiting.
Evidence that the applicant has sufficient and stable resources, as analyzed below, derived from a stable or satisfactory income of the applicant outside the Republic. Income includes salary, pension, deposits in a bank account abroad, rents, dividends, interest on deposits or by exception from dividends from a company in the Republic (with certification by the Company's Accountant that he does not receive any salary from his position) or rents in the Republic , or from income in his bank account in the Republic from a salary from his previous work in a company of foreign interests.