No, all their spells costs same mana as normal.
To fill their spell quickly, make as many matches as possible, including their mana color if you can.
Enemy get mana from every match you made and every gem you destroyed via match. Gems with the same element just fill a bit more than other gems. I can easily fill a 50-mana spell in one turn or even twice in a row if starting board isn’t weird enough to prevent lots of moves.
Some of their spells charge slower just because they have a higher mana requirement.
Edit: After hours of testing in dungeon I know how enemy gain mana:
If no other factor exists,
They gain 2 mana from every gem/skull you matched.
If that color is their weakness, they only gain 1 mana every gem.
If that color is same as their element, they gain 3 mana every gem.
No extra effect if that’s the color they’re strong against.
BIG gem count as if that many gems are matched FOR YOU. Enemy gain mana as if it’s a normal gem.
Remove, destroy and explode won’t charge enemy mana at all, no matter who did that.
If enemy is an orc,
FIRE gem give him 3 mana,
ICE gem give him 1 mana,
Other gems and skulls give him 2 mana.