Hi zullup,
it seems that C4D is not capable to read the UV data from the Alembic object, there are no uv tags, so you should have the same behavior with any render engine inside C4D.
Since Standalone can read the uv data correctly, you can set up the hair in Standalone, save as package (orbx), and import it back in c4doctane with ORBXLoader object:
https://docs.otoy.com/cinema4d/ORBXLoader.html
ciao,
Beppe