I welcome and look for, during weight resistance training or when using stairs as a training tool, subtle shaking during eccentric contraction at 'sticking points' (weak areas along the muscle being trained) and is an indication of neural impulsing motor unit recruitment, that muscle is being built.
Going down stairs is eccentric motion that also elicits tremors. Each step down a stair is an opportunity to harness eccentric resistance using body weight and foot action to guide the descent. Deliberately peel each foot from each stair keeping them pointed straight takes them through full range of movement working calves legs and butt. Foot peeling forces a controlled decent, and a longer stance on each leg revealing the sticking points. Breathe though the tremors, with time the descent will be more solid.
For those who get winded ascending stairs a concentric contraction lifts the body upward. Each concentric motion upwards acts alternately as a one legged squat upward when pressing off the heel-butt connection. A two part breathing cycle to a two part step up prevents being winded. The tremors are less obvious on the concentric ascent but it is still possible to tune in to the resistance.
If the subtle shake occurs you know you are getting to the deeper layers and actually building muscle which will be apparent as the legs become stronger and more cohesive to your gait.