"In Theatre" has always been widely interpreted. During the Falklands War the guys on Ascension subsequently got the South Atlantic Medal, but without the rosette which indicated service on The Falklands or the surrounding waters. Not a lot of risk, but a reasonable amount of rigour I assume.
The same criteria would appear to have been used for those in Cyprus during GW1 & 2 - though I would suggest the amount of rigour was pretty variable!