The Longman Dictionary of Contemprary English says, for extent,
how large, important, or serious something is, especially something such as a problem or injury; It is too early to assess the full extent of the damage.
and for magnitude,
the great size or importance of something; They did not seem to appreciate the magnitude of the problem. (and also) the brightness of a star; the force of an earthquake
So both magniutde and extent can apply to size and/or importance.
The difference is somewhere else: it lies in the adjective 'great' (Latin 'magnus'); with extent, the people estimated the size and/or importance of the disaster to be great or small – we do not know – but it was greater than they tought; with magnitude, the people estimated the size and/or importance to be great and it was even greater than they thought.
Earthquakes and stars, even if their magnitude is small, still involve incredibly large/great amounts of energy…