Do charge controller & inverter's builtin charger "conflict"?

I'm designing a small (600W using 3 200W panels in series) off-grid system.

Current plan is the Apollo T80 charge controller, Outback VFX 3648 inverter/charger/AC transfer switch, and a single string of batteries @ 48 V.  I plan to use a Midnite Solar E Panel to hold breakers & tie it all together.

I actually have grid access, so I'll tie the grid into the Outback's AC input.

I plan to attach smallish loads to the Outback AC output, such that I shouldn't need to pull AC from the grid very often (only after several days of rain, maybe).

So ... here's my question: how does the charge controller (T80) and the inverter's charger "agree" on who should do the charging, when?  What if they both try to charge the batteries at the same time (and perhaps disagree on whether it's time for bulk vs absorb vs float)?  How can I configure the T80 and inverter to not step on each other?

Thanks!