The Cyrix is not a permanent connection between the service (house) and starter battery. It is a voltage-controlled relay. When the service battery (connected to the Multiplus) is being charged and its voltage rises above a threshold, the Cyrix closes and parallels the starter battery positive with the service battery positive. In that state, yes, the starter battery is effectively connected to the Multiplus charger output (through the Cyrix). It will receive charge as if the two batteries were directly paralleled. Once the charging source stops or voltage drops, the Cyrix opens again, isolating the starter battery.
The starter battery is only paralleled when the service battery is charging (or above the Cyrix threshold). It’s not a permanent connection. Because the connection is direct parallel, you must not mix different chemistries or sizes as “main service batteries”. But a small starter battery being topped up is fine – it only receives a maintenance charge. The Multiplus’s charger profile is always optimized for the service battery type. The starter battery is “along for the ride,” but since it’s usually an automotive lead-acid, it tolerates this just fine.
The main problem with interconnecting batteries of different chemistries is the different float and absorption voltages, and to a lesser extent, the possible requirement for equalisation charge and the voltage required for that.
However, Wet lead acid and AGM share very similar voltages, with the exception of equalisation - for most AGM types equalisation is not permitted.
Given this, then there is generally no risk of paralleling them during charge. You really need to study the manufacturer’s recommendations for each battery type.
4 cells of LiFePO4 have very similar voltage requirements to AGM, BUT with the added requirement of cell balancing - to be provided by a BMS unit.