KMeans clusterization on documents
Let us assume that your corpus has n distinct keywords. For a k-means algorithm, each keyword is an axis in n dimensional space. Document is a point in that n dimensional space. 

K-means algorithm will allocate each point (a document) to a single cluster. When you say a keyword is appearing in two clusters, it probably implies: that particular dimension/keyword is important for both clusters.

Let us take hypothetical example: if you have a patient's blood pressure, cholesterol levels and bunch of other medical parameters. Let us say you discretize blood pressure to 2 or 3 levels. If you run k-means on this data, each patient will be assigned a unique cluster. But it is quite possible that two (or even more) clusters all have patients with > 120 systolic blood pressure.

You need to probably read the results of the k-means more carefully.