I can't really answer where the cyprus iron age kingdoms originated from but as for your inquiry, we do have to establish first whether the trojan war as told by homer actually ever happened at all

https://www.reddit.com/r/AskHistorians/comments/70698n/why_do_some_historians_completely_dismiss_the/dn1cftl/

By /u/Iphikrates

https://www.reddit.com/r/AskHistorians/comments/1i0goq/what_evidence_is_there_on_the_trojan_war/cazyc2m/

By /u/xenophontheathenian

https://www.reddit.com/r/AskHistorians/comments/8y57q5/has_enough_evidence_been_uncovered_to_determine/

By /u/qsertorius

And if the trojan war didn't happen... Well they probably couldn't have settled cyprus