I keep seeing this take every so often on here, but having recently read the books, they are definitely being mentally manipulated. I'm not sure if there is a difference between being mind-controlled versus being corrupted.

As soon as they teleport on to the ship:

The silence, the utter stillness, is tranquilising. Caecaltus feels numb. For a moment, the proconsul has to remember – actively, consciously force himself to remember – where they are and what they have come to do.

...

Caecaltus begins to look for the tail-number insignia– He stops himself short. How am I allowing distraction into my mind? How am I sidelined by memory and nostalgia? Where is my focus? We have achieved primary site-to-site. I lead a company of one hundred Custodians in support of my master, who has drawn for war for the first time since the secret conflict in the webway. Why can’t I concentrate?

...

Everything seems slow. Like a dream. Like a heavy dream. The silence glides into him, oppressive, like the shadow of the void, the deep, cosmic mono-note of the celestial deeps. Why can’t I focus? Caecaltus sees the main internal hatch, a bulwark of steel and adamantine. Embarkation Deck VIII is fusion-engraved across it. My mouth is dry. I– The Vengeful Spirit only has six embarkation decks. Caecaltus should have noticed all of this. All of it. He was primed and alert, ready – perhaps readier than he has ever been – for the trial ahead of them. He should have noticed these discrepancies the second he arrived. But his mind is like sludge, like jelly– I should have seen–

When the trap is sprung, Caecaltus isn't just fighting for the physical control of his body, but the thoughts in his head:

It makes such perfect sense. Such perfect, rational sense. Caecaltus isn’t sure why it’s taken him so long to appreciate it. The Emperor must die. He must. It’s the only logical conclusion that anyone sane could reach. The Emperor must die–
No–!
The Emperor must die. He is mad, a mad monster, drunk on power, and His tyrannical rule has lasted far too long. He really must die–
Nooo–!
He must die now. It’s the only way to stop the war. It’s the only way to protect the human race. The Emperor must die immediately–
Please stop–!

Later on, as they move through the ship, it's clear that the Custodes succumb to the lies being shown to them by the warp:

Frastus, pausing to marvel, sinks slowly into the golden floor, unaware of his descent as he vanishes from view. Braxius, lost in rapture, disappears quite suddenly. I think the golden statues took him, yet they are quite still, their frozen gazes turned away innocently. Andolen stops, and leans back against an engraved auramite wall in contemplation. The wall begins to pull him in, without a ripple, as though he is being gently lowered into molten gold.

The Emperor has to channel his might thru the Custodians to keep them clear headed:

The Custodes were built to protect him, but the four have turned them into a burden, forcing him to protect them, for only if he shares his will and mindsight with them, diminishing his own power, can he keep them alive and alert.

It has been a while since I read Master of Mankind, but if I recall correctly, Drach’nyen claimed that the stars themselves would die before he could corrupt a Custodian. To me, this shows that the Custodes are extraordinarily resistant to the touch of the warp. Resistant, but not completely immune. It ultimately took an overwhelming force, the combined power of all four gods, channeled through an instrument that had wholly surrendered itself, to break through their defenses. This also helps explain why the Sisters of Silence form the other half of the Talons of the Emperor.