I can't give you a 100% answer on this
And I'm sure their supposed to be loyal to the King above all
But, I think they are more loyal to the Liege Lord, which is the guy that's actually in their region, and that they are more likely to deal with on a regular basis. And if war is starting, they trust their liege lord to make the right decisions regarding sides taken and tactics.
Let's say for example, that a small noble house in the North disobeyed/turned against the Starks. The Starks could rally the Northern houses, and remove that family. A new noble house could take up on what you used to rule, and the old one is dead or cast down. I'm not saying a King couldn't do that too, but the threat of your Liege Lord's wrath is a lot closer than the King's. And you better not disrespect the King and get your Liege Lord in trouble.
Now two examples of lesser lords siding with the King over their liege lord in the war, the Boltons and the Freys. And both are seen as dishonored. IMO the Freys are perceived with even more dishonor than the Boltons for breaking guestright.
The Freys kill Catelyn Stark (Tully) and Robb Stark. The Boltons also participate in this act. The Freys Liege Lord was Catelyn's father. The Bolton's liege lord was Robb. Obviously, we see where those two families end up (The North Remembers). In the show, Arya takes bloody vengeance and Jon/Sansa kill the Boltons.
These families went with the King instead of their Liege Lord because each of them was going to be made the new Liege Lord. It was just to good to pass up.
In the show-
Now in the case of Randall Tarly, I don't believe that he would be perceived that poorly for his actions in the show. Olenna is old, like near death old, with no heirs. It would be stupid not to take the Lannister's offer. I feel like most of the Reach could understand that.
But in the books
This would be more difficult to pull off. Even if Margaery and Loras Tyrell are dead, Loras is the 3rd son, not the only son. His older brothers, Willas and Garlan, are at Highgarden and can carry on the Tyrell name. I feel like a lot of the Reach would stay loyal to their Liege Lord, the Tyrells, with two Tyrell men and Olenna left alive.