vsftpd should run as a service, not when you are logged on.
Now if you are talking about when you are connected to the internet, then yes you will have that kind of trouble. You must be connected to the internet in order to access vsftpd from another location.
One other thing, if you are operating vsftpd with anonymous upload and download access inside an internal network then that is ok. Otherwise this configuration is very insecure. This means anyone can upload their stuff.
are you sure you want that?