Ok, here is how I did it(don't know if there is a nicer solution):
[[test]]
name = "test_cionc_parser"
path = "src/parser/lib.rs"
[[test]]
name = "test_cionc_utils"
path = "src/utils/lib.rs"
That's in the root Cargo.toml. You basically tell it to create tests for the other crates.
Edit, removed:
[[test]]
name = "test_cionc"
path = "src/main.rs"
since it already creates and runs a test for this.