This isn't unique to Cyprus. Deloitte Global is specifically structured this way:

"The member firms are primarily organised on an individual country or regional basis and each operates within the legal and regulatory framework of its particular jurisdiction(s). They are separate and independent firms that have come together to practise under a common brand and shared methodologies, client service standards and other professional protocols and guidelines."

https://www.deloitte.com/ce/en/about/governance/network-bran...