I also don't think there will be a civil war in the Empire.
As true as it is that the emperors sever ties with their houses when they move to join the Emperor Family, that doesn't mean that their home house don't benefit from their rule. House Sarum is on top right now, and they're not going to stand against Jamyl to threaten that. Personally I frowned when House Sarum were providing security for the
514 Summit, but it goes to show that Jamyl definitely has her home house on her side.
Aritcio Kor-Azor has been made Imperial Chancellor. I don't think Jamyl would have made him the third most powerful individual in the Empire if she had suspected him to lead a rebellion. However, it could also have been a way to purchase his loyalty - or a way to keep him too busy to plot against her. As Imperial Chancellor, he not only has to prioritize matters of the Empire over matters of his house, but if he would rebel it's possible that many of his vassals would consider his abandonment of the office to be ruining their own influence in the Empire. The fortune of House Kor-Azor is very much tied to the Throne.
Catiz is progressive and benefits greatly from Jamyl's reign. Jamyl should recognize her as a good ally, and treat her accordingly. This may be the first time the Udorian house is treated fairly, or more than fairly. It's unlikely that the Tash-Murkon would turn against the throne.
House Kador was neutered when Jamyl confiscated their fleet. Even if they rebel they don't have anything to rebel
with. The move would have upset Kador and most of the other houses though. If the throne is actually going to enforce Heideran's Decree, it will be very problematic for the holders. Also, I guess it's possible that the confiscated fleet is still loyal to Kador, and if he rebels they would still rebel with him.
Ardishapur... Ardishapur is probably the only one who might be both inclined and willing to depose the Empress. Giving him the Ammatar Mandate doesn't seem to have made him much more loyal, but it's hard to tell. Giving heirs like Yonis and Aritcio senior positions in government means that they have a vested interest in keeping Jamyl alive and on the throne - because the minute succession trials are on the schedule, their odds of continued power (and life) are rather slim.
Returning the Khanid Kingdom to the Empire and giving the King a Privy Council seat was also a great move by Jamyl to strengthen her position. She's telling the other heirs: "If you're not loyal, I have others who are willing to fill your shoes." And Khanid is allowed to maintain his own fleet and army...
You have to keep in mind that the Heirs (as an institution) are used to ruling their domains for centuries before having to take the suicide lottery tickets. The current heirs are exceptionally inexperienced by imperial standards, and as Karsoth demonstrated they are more interested in ruling their own lands than pushing for the throne. The empire is all about stability. Changing rulers and Heirs several times in a decade has probably not happened for thousands of years, so the current heirs are much more inclined to be tolerant of anything that lets them be alive at the moment - not necessarily out of narcissism, but out of concern for the stability of the Empire and their own realms. That's why they tolerated Karsoth. That's why they voted Jamyl to the throne. And that's why they aren't kicking her off it.