I think either scenario can be true.
Edgar intentionally incites nobles to rebel so they can eliminate and suppress the discontent elements in the country. That's why he said the spy "can't find anyone who tries to cause disturbance". It was Edgar who advised against telling anyone else due to the lack of evidence, and also the one who guided the trio's actions.
For the spies, their loyalty to the former Falmuth royalty is just too high, as shown on various occasions when they appear. They still address Edgar as Crown Prince, despite Youm being decided to be the new king of a new nation that will replace Farmuth. Their reasoning can be to kill Youm and crown Edgar as the new king, while still allying with Tempest. They get to reinstate Falmuth Royalty as ruler without crossing any of Tempest's interests, like making allies.
You mean... except being solidly defeated by Tempest, and one of the conditions Tempest placed on Peace was to have Youm to be crowned King...
And that's even
before it being an expressed wish from Rimuru. With the realisation of that wish entrusted to a dere-dere Demon who has sworn servitude to said Rimuru..
The former Royalty
know this... So their definitely-not-ninja squad should be well aware of this as well.
Rimuru may be a ...manageable political factor... in their eyes, especially since Rimuru doesn't often use his full capabilties in public so they don't
know how insanely OP he is.
But that dere-dere Demon.... Very much present, fresh in memory, not known to beat around the bush that if it's something Rimuru wants, it happens, and
stays Happened. Or Else....