Alternator output does not go through solar controller. Most, but not all, solar controllers are designed for Solar input only; to do otherwise may destroy them. Alternator to house batteries are done either by 1) battery combiner relay, 2) DC to DC charge controller, 3) A/C inverter on car battery to D/C charger (or inverter/charger) on house, 4) probably more I can not think of. Each method has their proponents on this forum. Several threads go into details of options. Method 3 is Orton's style, which I copied.
2015 Transit Van Silver 3.7L 148 HR. DIY Camper.