The Sargent "charger" in these units is just a 13.8v regulated linear power supply, it has no knowledge or adaption to the battery it's just set at the nominal classic charging voltage for a regular flooded lead acid battery. By a quirk of chemistry these battery types will sort of self regulate so long as the "charger" doesn't supply too much current (1/10th of the capacity is the usual figure). And yes being a linear power supply it will get hot under load. The word you are looking for here is "cheap and basic"...
Using it with an AGM isn't ideal as AGM's usually needs a higher charging voltage, but it's unlikely to do any harm they just won't fully charge and there is an argument that if you are split charging from the vehicle it's better to match the battery types starter<>leisure though using a proper DC-DC charger is miles better.