The way it is wired now is a common way and not problematic. It will only run when the thermostat is calling for heat. The furnace fan runs after the call for heat ends in order to cool down the heat exchanger and get the most efficiency out of the unit. That time is adjustable on some control boards but left alone is usually best.
The note is telling you that it can be wired to the fan leg of the thermostat and it will run when you set the fan switch to "On" at the thermostat and not "Auto." I don't recommend doing that since the humidifier doesn't work very well when the heat is off and will waste lots of water.
You should check to see if it is connected to hot water (recommended) since that makes it works much better than a cold water connection.
The note is telling you that it can be wired to the fan leg of the thermostat and it will run when you set the fan switch to "On" at the thermostat and not "Auto." I don't recommend doing that since the humidifier doesn't work very well when the heat is off and will waste lots of water.
You should check to see if it is connected to hot water (recommended) since that makes it works much better than a cold water connection.