How tuners work....
Barrel vibrations start before the bullet reaches the muzzle. The muzzle traces out some kind of arc, the shape of the arc probably being a little different from rifle to rifle. In most cases, I think the arc is an ellipse. The function of the tuner is to adjust the natural vibration frequency of the barrel "whip", so that bullets exit at an optimum point on the arc.
When the muzzle is on the side of the ellipse, it is moving fairly fast, and a small difference in when the bullet exits the muzzle will make a big difference in where the bullet lands. When the muzzle is on the end of the ellipse, it is moving slowly and a small difference in when the bullet exits will make very little difference in where the bullet lands. When adjusted to this point, the result is "robust". That means that small changes in charge, temperature, etc., usually make little difference.
"Barrel harmonics" is a misnomer. Resonant frequency is probably a better term. That is the frequency at which the barrel naturally vibrates. Barrel harmonics is probably a corruption of harmonic motion, which simply means motion that repeats itself. A harmonic of a frequency is an exact multiple of the resonant frequency.
Just putting a weight on the end of a barrel will tend to reduce barrel whip, as will putting vibration damping material in the barrel channel. Barrel tuning devices work a little better, but are very hard to set up correctly. Probably the best method is one of the ladder methods. The smallest groups tend to occur when the center of the group has moved as far as it is going to, and is ready to start back toward the starting point.