You can spray only or spray AND inject.  The beetle lays eggs in the crown.  These hatch into big horrible larvae (about the size of a witchety grub).  These bore holes (tunnels) through the interior of the trunk and leaf bases which causes enough damage to kill the trees.  I inject and spray big trees and just spray small ones as there's often no trunk to inject.  You could also apply the diluted chemicals as irrigation which MAY have the same effect as injecting.  If you Google Red Palm Weevil, there's a stack of info out there.