LotR3-RotK-Seq03

[Elladan and Elrohir]

Well, you gotta remember that in the book, Sauron was attacking Lorien, Mirkwood, Dale/Erebor, and Gondor all at the same time. Obviously, since Gondor was his nearest, his most hated, and arguably his strongest military foe, it would get the brunt of his blows. Gandalf knew that Minas Tirith was the key to everything ("If Minas Tirith falls, or the Ring is taken, the Shire will be no refuge.").
The Gondorians were obviously fully cognizant that Sauron's attack would come soon. I believe Faramir mentions something of it to Frodo, and of course Beregond also talks to Pippin about it.

So yeah, I think it probably was just common sense, in the book. In the film Gandalf has to have it spelled out to him by Saruman and the palantir.