BootMagic is a 3rd party boot manager.
EasyBCD is not a boot manager.
EasyBCD is an app to help you organize the Microsoft BCD
Microsoft bootmgr boots your system, not EasyBCD
EasyBCD is not active while your system is booting.
It is not active after your system boots either.
It only becomes active when the system is running if you start it.
Even then, it doesn't do anything unless you tell it to.