I'm not sure why or how McGonagall knows: possibly, in a departure from canon, she was conducting Trelawneys' interview instead of Dumbledore himself.

Yep:

The old wizard's face turned grave. "The same reason it must be kept secret, Minerva. The same reason I told you to come to me, if Harry made any such claim. Because it is a power that Voldemort knows not."

The words took a few seconds to sink in.

And then the cold shiver went down her spine, as it always did when she remembered.

It had started out as an ordinary job interview, Sybill Trelawney applying for the position of Professor of Divination.

[Snip prophecy]

Those dreadful words, spoken in that terrible booming voice, didn't seem to fit something like partial Transfiguration.

"Perhaps not, then," Dumbledore said after Minerva tried to explain. [...]