As it is right now the Klingon Defend Empire missions (Khaless Expanse / Azure Nebula) are a cross between Exploration missions and Federation "Enemy Contacts" but without the ability for other (non-teammates) to join in the "Enemy Contact" style battle.
The player goes to a cluster/nebula and scans anomalies until an Enemy Fleet is found, and upon entering the battle it is set up exactly like the Enemy Contact sector map on Federation: Destroy X squadrons with a reset timer. But unlike the Federation Enemy Contact, there is no way other players can join in the instance, as there is no indicator on the cluster/nebula map that there is a battle in progress. So, in effect, the player is always soloing an entire map of squadrons.
Suggestion: make a map indicator once an "Enemy Fleet" is found, or, upon finding an "Enemy Fleet" the player is placed into the instance of any ongoing battles.
Edit: To be clearer about the mission type and non-teamed
You can join...our fleet members do it all the time.
Just team up, go to the expanse your team mate is in and you usually get a tab on the side of the screen to join the mission. Sometimes you may have to do scans of your own before it will bring you into your team mates mission.
I will point out this works only about 95% of the time. Sometimes it won't and you still have to wait for your team mates to finish before you can join them.
Thought about reporting this as a possible bug, but figured if they havn't found time to fix simple things like being able to turn in the War Zone missions to Lt Menbat on Ganalda station, (it incorrectly tells you to trun them into Lt Mara on Qonos) which is a bug reported over and over since BETA, that it's probably not gonna be fixed anytime soon. They have more important things to work on, like Bridge interiors that you can look at if you pay extra for them so you can imagine what it would be like to actually do something there, costume pieces you can wear while you're "off duty" and knee high boots so you can...I donno...walk...
As long as it works good for the Feds, since Klingons were, in the Developers' own words, "put in to compliment the Federation" I'm sure it'll be fine.
*EDIT* and as soon as I got done posting, realized you're talking about the original Expanse missions, not the added exploration missions...sorry...
You should still be able to join your team mates instance if you team with them first, again, we do it all the time. Your team mates will even benefit from your previous progress.