Phoenix Smart IP43 Trickle Charger

Wiring up the Phoenix Smart IP43 trickle charger to charge a start battery. The primary output charges the house bank.

I notice the trickle charger output has both positive and negative terminals. Is it best to run a dedicated ground wire to the aux battery that I’m trickle charging, or can I wire this to the common shared ground?

Diagram from the IP43 manual shows a dedicated negative, but now sure how literally to take this recommendation: