Multiple chargers - even if they don't talk to each other - don't butt heads or confuse each other. None of them actually know what the battery state of charge is. They each read battery voltage and do what they do based on that.
It's like having multiple compressors hooked to one big air tank, and each compressor has its own pressure switch. If the pressure (voltage) is low enough, all the compressors (chargers) are pushing air into the tank. As the pressure rises, whichever compressor has the pressure switch with the lowest setting stops pumping air into the tank, while the compressor with the switch with a higher setting keeps pumping.
Of course, chargers also have timers, to hold a higher voltage for a while after the battery reaches that point, to allow the battery to slowly absorb all it can. Holding a high absorb voltage doesn't much matter for solar or dc-dc...it stops when the sun goes down or the engine shuts off. It matters for shore chargers since you don't want to hold absorb voltage for days non-stop.