The singing rod works via stick-slip forced vibration leading to resonance similar to a wine glass. However, the natural frequency of the rod is higher than the wine glass, so you need rosin to make your fingers more sticky rather than more slipprey like in a wine glass. This is rather more detailed than you will probably want.
One note, the first site at the Whelmers suggests that the singing rod is vibrating transversely. I'm pretty sure that's not the case. Put the end in water and you will see the water making concentric circles which looks quite a bit different than what a tuning fork looks like in water.