Does layer always appear in every chain

No — layers and the Chain are separate game systems, and one does not imply the other.

Layers (CR 473–480) are the evaluation framework for how Game Effects alter traits, abilities, and numbers on objects. They run as part of continuous characteristic evaluation — whenever an effect needs to be applied, a chain or not. The Chain (CR 327–331) is a temporary zone that only exists while a card is being played or an ability activated.

So a Chain can form and resolve with zero layer activity (e.g., drawing a card, dealing damage), and layers get applied constantly outside any Chain (passive auras, buff counters, Combat Cleanup). The two only interact in that a resolved effect may cause a layer evaluation — but layers are not a Chain item, step, or event.