I don't know if the vaccination can cause it or not. I do know that the vaccination is not 100% effective in preventing a cat from getting FeLV.But he did have FeLV injected to him, twice (talking about vaccinations). Maybe they caused the infection?
I focused in on FeLV and FIV only because I found no information anywhere that suggested using Zylexus as a immno-stimulant for FHV or FCV. But, that doesn't mean that vet's don't use it to try to boost the immune system for cats with these viruses as well; and perhaps that may be a more preferred treatment in Turkey, as opposed to the US.What made you think that this is FeLV or FIV? It could also be FHV or FCV.
Was your cat ever vaccinated for FHV or FCV? Did the vet ever suggest a PCR test for any of these viruses? I believe they can be confirmed through a PCR even if Count received vaccinations for them, although as with most tests it is not fail-safe.