I made my objectives display with the O key instead of Tab. Here is my code if you want to compare to yours. This script I named imp_df_l1obj01display.fpi but you can call it whatever.
;Artifical Intelligence Script::::::::::::::::::::::::::
desc = Shows Objectives Text HUD (When O Key Is Pressed)
;Triggers
:state=0:hudreset,hudx=50,hudy=30,hudimagefine=gamecoretextimp_df_l1obj01.tga,hudname=objectives,hudhide=1,hudmake=display,state=1
;O Key Pressed
:state=1,scancodekeypressed=24:state=2
:state=1:hudunshow=objectives
:state=2:hudshow=objectives,state=1
;End of Script
Hudname, hudunshow, hudshow should have the same name. I also created the TGA hud to display the text in my objectives.
I call this script with a trigger. In the main field I put this script. I place the trigger anywhere in the map I made.