I spoke to my colleague and he said the law changed in 2009 and that's when they started participating in the conscripted service.
i just googled Cyprus 2009 Jehovah military ..... and indeed there seems to be evidence he was being truthful.
Obviously it's just anecdotal, but I do believe my colleague as he had no motive to lie.
https://www.wri-irg.org/programmes/world_survey/country_report/en/Cyprus
"25 Sep 2009 β warresisters
Issues
- Cyprus still maintains conscription. The recognition of the right to conscientious objection does not meet international standards.
- The right to conscientious objection is not recognised for professional soldiers, nor for serving conscripts."