It sounds like you are conflating the location and security modes. Your SmartThings ‘location’ has modes, sometimes explicitly called the ‘location modes’, that you can use as a sort of global status flag in automations. They default to ‘Home’, ‘Away’ and ‘Night’ (you can rename them and add to them).
The SmartThings Home Monitor (SHM) is a smartapp that has its own internal states also called modes that are sometimes referred to as the ‘security modes’ in an attempt to resolve the confusion caused by calling them modes in the first place. I only have the SmartThings Classic app and in that they are called ‘Armed (Away)’, ‘Armed (Home)’ and ‘Disarmed’. SHM in the ‘new’ app (which I’ve never seen) is a completely separate smartapp but I believe uses the same name for its modes, or something very similar.
So when you are setting the modes to ‘Home’ and ‘Away’ you are setting the location modes and the SHM modes will not be altered.
Although I’ve never seen it, let alone used it, I believe that the ‘new’ app doesn’t allow you to arm and disarm the Smart Home Monitor by anything other than time of day or manually.