Some insight is given in the Foreword to the Atlas as well as the Acknowledgments.
In the Acknowledgments Karen Wynn Fonstad acknowledges several Geographers, Professors of cartography, as well as University Archives with "Tolkien Manuscript Collections". From this we can gather that she used notes from Tolkien and his original maps to create maps using her cartography skills as well as that of other experts in the field.
In the Foreword she discusses how her maps in the original edition were based strictly off of an analysis of written text.
The maps detailing the lands of the earlier ages, especially those in volume four, The Shaping of Middle-earth, were especially helpful in remapping the whole of Arda. In the original atlas the world maps were based strictly on analysis of the written text
She also states there were some sketches available from University archives.
In the volumes covering The Lord of the Rings, one crucial role of The History was the assignment of the various drawings and maps to the appropriate version of the text. This information immediately clarified why some of the sketches that had been available from Marquette University archives during the initial writing and design of the atlas differed in some details from the published descriptions...
In the Introduction Karen states the following:
Tolkien's original maps and illustrations have been utilised as a general references for location and elevation; but if differences arose, the final drawings were usually based upon the text and inferences drawn from it's passages.
This seems to suggest again that it was a mixed use of Tolkien's drawings and an analysis of the text.
That is all the information we get on the atlas but seems to agree with what Tolkien Gateway has to say on the matter. Which as Voronwë points out, has a complete list of their inaccuracies.