Paradoxically, fine-scale layering like that is more likely a sign of distant volcanic activity being blown in on the winds or just generally spread about. Ash can travel for thousands of km on Earth and studies of Mars suggest similar distances, despite the thinner atmosphere, especially for fine dust.

A local activity would give coarser grains, including the pea-sized gravel called "Lapilli", caused by ash clumping into balls in the humid volatile-rich cloud above the volcano as the eruption cloud cools. On mars, this would likely occur at lower altitudes and more proximal to the vent, but it would still occur - think of it as VERY dirty volcanic snowflakes!

As regards timing, just about everything we see at the surface now is relatively young compared to the formation age of the Gusev crater, but Mars does have a habit of deep-seated volcanism becoming localised in one spot for long periods of time, so your idea is certainly credible.

We still have LOTS to learn about Mars...