I'm pretty sure that's a bug. They are yelling those lines because Bunker Hill is a town under their protection and the place where they take Synths before moving them elsewhere (not to mention that it's probably also their main source of income).
Though they don't have such a good grasp on the town because all their caravaners are Institute informants. Stockton should work on his employee selection...
They are my second favorite faction because I like their character and their spy theme. But their ending is my least favorite and I don't support their cause, morally or pragmatically.
Desdemona would agree, yes.
And then you would find out how betrayal feels, just like what Father learns at the end of the Railroad route. Once you returned to the Institute after destroying the BoS, you would find out that Tinker Teleported the Railroad in and they started killing people.
You see, Desdemona does not trust you to be able to control your minutemen, which is why she passionately rejects any idea of allying with the Minutemen and downright forces you to choose Railroad over your own Minutemen in order to continue with the Railroad route. She would trust you with the Institute even less and would use this opportunity to destroy the Institute and save the Synths.
Also, nobody knows as much about evils of the Institute as the Railroad does. They are the least likely to trust them.
You can either lie to Shaun with a Charisma check or admit the truth and not be hostile to Shaun in the conversation that follows. I saved the Synths, admitted it, disagreed with Shaun more often than not n all quests and he still died telling me to make my own place rather than try to imitate him.
Mama Murphy reveals that you save the humanity, however you choose to define it. So if you consider Synths humans, you save them.
The only problem is the "Every sacrifice an acceptable lose" lien which practically tells you that the future of the Director Survivor will be a rocky ride (which is not surprising as there is too much bad blood between Institute and Wastelanders for it to be fixed so easily).
Yellow Director - loyal to you. If by some miracle she disagrees with your policies, she is the member of the least prominent department so little damage is there to be done
Justin Ayo - ambitious and would no doubt like to remove you... thankfully you can frame him and get him kicked out of the Institute, thus also getting rid of the only evil person on the board and the one responsible for 90% of evils the Institute did on the surface and inside the Institute
Alam Binet - believes Synths have souls so he will support many of your pro-Synth policies. Also, he will be replaced by Liam with time
Madison Li - wants the Institute to use its technology to help the people of the Wastelands. She will happily support your pro-wastelander policies
Biotech Director - in a random conversation with his second hand, he reveals to be sympathetic to Wastelanders so he will not oppose your policies. And if you are the Minutemen General, you can make his experiments easier by letting him do his work on some of your farms
She won't. Madison LOVES using science for the good causes. She is a very idealistic woman.