Indian Mock Strawberry (Potentilla indica) can contract a rust, yes, though the rust fungus in this case is not the same species of rust that can infect turfgrass, nor does it infect true strawberries (Fragaria species). There are many species of rust, and superficially, most look identical to each other, even though they infect different host plants. There is no curative fungicide for rust, nor would treatment be recommended for an invasive plant like Mock Strawberry.

This particular rust infection didn't come from the asters, though, nor would it move back onto asters next year, as the rust that infects asters uses pine trees as its alternate host for part of the life cycle. (Rust fungi that use alternate hosts bounce back and forth from one to the other, so the spores on aster are intended to infect pine, and spores on pine infect aster, so they don't move from one aster-family plant to another. Plus, strawberry and potentilla are in the rose family, not the aster family. Roses can contract rust, but we don't think it's the same species as the rust infecting the Mock Strawberry.)

Miri