Joined Trill being on the side of the KDF has a precident, but it has never been depicted. Considering that Joined Trills (and this part is canon) consider the wellbeing of the symboint before the host, it makes little sense to join an empire that sends their troops out to die regularly. Starfleet is an exploratory corps, STO just turned it into a millitary, the KDF was pure military organization.
Dax, well, being Dax and having 2 seperate hosts involved heavily with the Klingons, it was only natural to go that route with the character. But on principle, the whole "protect the symbiont" thing flies in the face of being part of the Klingon forces.
Actually, that situation makes it super easy to explain. All it takes is a trill colony and an undine threat to that colony. Mix in Starfleet's proven horrid track record with dealing with the Undine and the Klingon's way of stepping in from time to time to try and save the Federation from its own incompetence and, blam, Trill colony winds up under Empire protection, in part to protect the symbionts. Doesn't even have to be a colony, really, could just be a ship full, abducted by undine due to Federation incompetence, saved by Klingons.
And just like some joined Trill join Starfleet, some joined Trill join the KDF.
Oh, and as to saying the KDF is more dangerous than Starfleet, just watch Voyager and see how many crew members that Captain gets killed due to being stupid. Check out the life expectancy of non main cast away team members on DS-9. Seriously, they make red shirts look to have high survival chances. And then there's the whole Starfleet poke something to see what happens because we're bored otherwise mentality. Life in Starfleet isn't exactly safe either.
Well one idea to consider is that the Dax symbiont itself predates the federation by almost 150 years, and we have no idea how long they live. Dax might not be the oldest symbiont, so with that background its reasonable to believe that not every symbiont 's 1st loyalty will be to these upstart Federation types. Their government is not yet even 300 years old. A mere blink of an eye in an interstellar time frame.
I have been watching DS9 trying to catch up on all my Trek history and I had thought that the reason why the KDF had the joined trill was because of Jadzia and Worf but at the end of season 6 jadzia is killed. Now I still have to watch season 7 so maybe my answer is there but I don't mind spoilers so can I get the canon reason for the KDF having Joined Trill or was it just to even things out.
I have a trill KDF so I'm not trying to be hypercritical here or anything just a question of curiosity.
In all honesty, the Klingon players felt left out and so Cryptic caved in and allowed Joined Trill to join the KDF (not sure why regular Trill are still Federation only).
Cryptic's justification was basically saying there was nothing that stated Trill was a Federation World and could be regarded as Neutral and thus can be on both sides.
Storm is 100% correct and I like the answer, a real answer.
Jadzia is an exception. Just because one joined trill was great friends with some Klingons doesn't mean they all were. In fact DS9 largely hinted that Jadzia was the exception.
Sure, some Joined Trill besides Jadzia might be great friends with some Klingons but Joined Trill are already rare and I doubt there's more than a handful and none would likely be more respected than Kurzon was.
When you see whole fleet of Klingon allied Joined Trill let me know. Until then it is just a few independently minded individuals, which is possible within, if not exactly canon.