For the Dilgar Adventures I am running I crafted the Omega Incident to be the EF hyperion cruiser Promethius pulling border patrol and filtering / guarding / inspecting all the refugee ships coming through a specific jump point. The Pyrotannia entered earth space just a few hours before a Dilgar Destroyer. Captain Jankausky spoke with the Dilgar ship and would not let them take control of the Pyrotannia, a diplomatic vessel full to the brim with various diplomats from all the systems the Dilgar had forcibly taken.
The Dilgar seeing only one EF ship, and being overcomfident, prepared to fire, Captain Jankausky simply beat them to the punch. However the battle between the two ships cost the lives of thousands of refugees as large ships packed full of aliens only wanting to live peacefully were in the words of B5, "Blown to Hell". My players were a bit depressed after the adventure. Seeing all the innocents lost, doing the right thing by defending against the Dilgar, and then Earth Force showing up and punishing them all. One line I remember was, wait, when did we become the bad guys.
Earth Force learning of the actions sent ships to relieve the Captain of command, and to stand trial for his actions. The incident labeled OMEGA, was so labeled because once the Abbai diplomats gave their report to the Earth Senate, Earth went to war. Thus the 'Omega Incident' was the Last Dilgar 'Incident' and the start of Dilgar 'battles' and 'skirmishes'.
But that's just my personal take on it. To add to a bit, I believe earth dispacted a ship right after that into dilgar space. The Earth Force rulebook gives the name of the ship. Needless to say, it was blasted into tiny pieces. Yet another reason to go to war.