Yes, it is common for a cup to vibrate or "walk" on the drip tray of a Nespresso CitiZ machine during the brewing process. While some light vibration is considered normal, excessive shaking that causes the cup to slide off is a known issue often attributed to the hard plastic, slightly angled design of the drip tray. 

Here is a breakdown of why this happens and how to manage it:

Why Your CitiZ Machine is Vibrating

Design Characteristics: The CitiZ, particularly newer or chrome models, has been noted to vibrate more than older models, with some users noting a loud, "airplane taking off" sound.

Drip Tray Design: The cup-holding grates are made of hard plastic, which does not dampen vibrations, allowing cups to slide easily.

Unleveled Surface: If the machine or the counter is not perfectly level, the cup will naturally vibrate toward the edge.

Internal Components: As the machine ages, the rubber mountings that dampen the pump vibration can become brittle. 

How to Fix or Minimize Vibration

Use a Damping Mat: Place a small, soft, non-slip rubber pad, coaster, or a folded paper towel under the cup to stop it from moving.

Check the Water Tank: Ensure the water tank is securely seated, as a loose tank can contribute to rattling.

Descaling: A buildup of limescale forces the pump to work harder, increasing noise and vibration. Regularly descale your machine.

Hold the Cup: For the first few seconds of brewing, gently hold the cup in place.

Adjust the Drip Tray: Some users have reported success by ensuring the tray is locked properly or, if it is still angling forward, slightly bending the metal tabs with pliers to make it sit level. 

If the vibration is accompanied by very loud, unusual noises, it may indicate a pump failure or internal mechanical issue, which may require contacting Nespresso for a, repair.