You shouldn't have anything else to do as upstart read it's configuration at each boot.
You can try to check if the service is started at by the following way, after booting up try :
ps aux | grep hid_mapper
If it is not started, then your problem might come from the condition :
start on started udev
This means that remote mapper should be started once udev is started. Depending on your distribution it might not work. Could you tell me what distribution you are using ?
You could also try to get the condition of another script that runs after udev, for example gdm or kdm. Edit /etc/init/kdm.conf (for example) et copy the "start on" stanza. On ubuntu 10.10 it is :
start on (filesystem
and started dbus
and (drm-device-added card0 PRIMARY_DEVICE_FOR_DISPLAY=1
or stopped udevtrigger))
Then replace start on started udev in your current remote_mapper.conf by the standza you juste copied.