With a flow pulse at 0.1s period I'd expect convergence issues at 0.01s time step, so it's more likely that you're picking up something real at 0.001s step size. If you run fixed mesh how does the pressure field look with time? NonNewtonian fluids do interesting things to the flow, so you may find there's an unresolved flow feature somewhere.
You may also want to review the Fluent intrinsic FSI as the solid material properties look "simple" so you'll save time on the system coupling. There's a tutorial/video in Help which should explain most of it.
As an aside for the first two posts. 26th August was a Saturday, so you're not going to get an answer from Ansys staff: we generally don't work weekends. Bumping a thread after 5-6 hours won't speed up a response, and may delay it as it messes with one of the (Ansys) check scripts and is more likely to annoy (nonAnsys) people who may help rather than encourage the community to step in.
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