Whistles are transposing instruments. The fingering he wrote is the same for either. If you use a D whistle, it’s Em, if you use a C whistle, it’s Dm.
All of this depends on how far into music theory you want to go (which is a deep subject).
Here, we’re actually talking about modes rather than keys. I’m sure you understand what a major key is, but it’s the notes you need in order to make the western major scale (do, re, mi, fa…). Whistles in general are tuned to this scale, and come in different keys.
When you play the notes from bottom to top, you play the major scale. D major on a D whistle, C major on a C whistle, etc.
Next come modes. You can check them out here:
http://en.wikipedia.org/wiki/Musical_mode
If you look at the graphic there, you’ll see the modes listed. Notice the Roman Numeral after the name? That gives you the position of the starting note.
So in the key of D (D whistle), if you start at the bottom note (all holes covered) and play the scale, you’ll get the Ionian scale (major scale). If you start at the second hole (one hole showing - playing an E), and play the scale straight up the whistle - same NOTES as last time, just starting on E instead of D - you’ll get the E Dorian mode.
E Dorian is a minor-sounding mode. Keep in mind that this won’t be the modern, western D minor scale. For that, you’d need an F whistle (D is the relative minor - see below).
Back to D Ionian and E Dorian - the thing to note here is that these are in the SAME KEY (D), but because you’re starting (and ending) on different notes within that key, you’ll get different modes, and therefore different moods (major or minor).
Generally, the third note determines the overall feel of the mode. So, if the third note is minor (which is listed on the graphic at Wikipedia linked above), then the mode will have a minor sound.
In fact our western minor scale is the Aeolian mode, which is the sixth note of the major scale. This is why, when you look at the key signature (sharps and flats at the beginning of the sheet music), the key of C and the key of A minor are the same. A is the sixth of C, and is its relative minor. The key of F maj and D min are the same as well.
So with whistles, you don’t need to know the sharps and flats so much. Just know the key you’re in and use the appropriately keyed whistle.
Hope that helps (and doesn’t confuse you further!).
Jason