Password protection for My Passport for mac

I installed the security software last night and set the passwprd. Then I enabled the drive inthe Time machine for back up. everything went smoothly. I had problem ejecting the drive though even after quitting Time Machine, so I then had to shut down the computer and remove the drive. However today I reconnected the drive and the TM did its back up and then I was able to eject the drive normally. 

Thanks for the help!