Which Cesium demo did you try this with? For mobile, the best strategy is to make Cesium take up the full window, like it does in Cesium Viewer. You have to set the right meta tag to prevent gesture zoom:
Give that a try. Look at the source of Cesium Viewer for a complete example.
In other news, I just downloaded the latest Firefox for Android, and it looks like the Cesium globe is badly broken there, with flashes of random globe textures flying all over the screen. This was on an HTC Evo 4G Lte.