I'm really not up enough on the background of Traveller myself. Guess it's time we all read this:
http://wiki.travellerrpg.com/Third_Imperium
...the gist of which is that there is a giant over-arching Imperial rule that blankets all known systems of Man.
Space itself is so vast though that it's impossible for one governing body to legislate over all of it, so there is a certain amount of autonomy given to sectors which are in turn ruled over by local Imperial Barons. Within those sectors there are varying amounts of lawful/lawlessness systems though.
I should look at the sector that we generated and determine where the local seat of power is based on Tech/Law levels and types of government, though if you guys want to have some input on that I'm open to suggestion.
The answer to your question is yes. Even if you guys didn't serve side-by-side it's possible you were in the same service...either serving in the larger Imperial Navy, the local Baron's personal levy, or a single system's local defense fleet. Keep in mind that your homeworld isn't necessarily where you'll be starting the game proper. You guys all have to come together at some point somewhere. I'll leave that up to you to decide which of these systems you'd prefer to start your careers from.
EDIT: Actually the sector capital is 6-3. It's the only system that has a 9 for governance (Imperial Bureaucracy) as well as having an Imperial Consulate base. Thank you RNG.
Fun map note: Azari your homeworld is a feudal technocracy. Which means it's ruled by a bunch of scientists and technicians who have given themselves royal titles and use their labs like fiefdoms and treat their lab technicians and workers like serfs.