Normal Gem is consumed in the process of applying its multiplier in the damage formula, so it only applies if the move happens to be Normal-type when you get to that step. If a calling move replaces the original move with something else that's not Normal-type, or if an effect changes the move type itself away from Normal, it does so before it ever touches the damage formula, and that check will not see it.
Some examples may be in order.
Things that do trigger Normal Gem
Using Assist (a Normal-type calling move) with Infernape and getting Judgment
Using Mirror Move (a Flying-type calling move) with Pidgeot and getting Revelation Dance
Using Thunderbolt with a Delcatty whose ability is Normalize
Using Weather Ball while no weather is in effect
Things that don't trigger Normal Gem
Using Assist with Spinda and getting V-create
Using Hyper Beam with a Sylveon whose ability is Pixilate
Using Weather Ball while there is weather in effect
Using Fake Out when it's not your first action (because the move fails before it gets as far as calculating damage)
Using Return right after the opponent used Protect
Using any move against a ghost (unless something negates the immunity, like Ring Target or Scrappy)
Using any move while Ion Deluge is in effect (if it would have been Normal-type before, it's Electric now)