OK. I think that I have got this straight.
Edwin Cairncross' five-year hitch in the Terran Space Navy was from some time in 3035 to some time in 3040. In 3035, A'u, a large amphibious agent of Merseia, while stranded on Nyanza, incited one Nyanzan ruler, the Sheikh of Rossala, to arm and prepare for insurrection. Somehow, either A'u or Rossalans acting for him got a message to Merseia. The plan was:
other nations, knowing that Rossala is arming, arm themselves in case Rossala aims to attack them;
a Rossalan harpoonist assassinates the Imperial resident, thus ensuring that there will be no effective space traffic control until he is replaced;
Merseian ships will arrive with heavy weapons;
Rossala will call on other nations to support the insurrection;
any rulers who refuse will be assassinated and replaced.
Although A'u himself is a brilliant organizer, the Rossalans are inept conspirators so that, when Flandry, alerted by Tom Umbolu's dying words on Brae, arrives on Nyanza, he easily follows the trail of the conspiracy. Flandry unites the rest of Nyanza against Rossala, hunts down A'u and speaks of laying traps for the expected Merseian gunrunners. It is at that stage that the Naval forces in which Cairncross is serving will come to be involved.
Thus when, in A Stone In Heaven, Poul Anderson, summarizing Cairncross' career to date, mentions a five-year hitch involving both suppression of a Nyanzan revolt and the Syrax confrontation, this summary fits perfectly into the Chronology of Technic Civilization.