Alucio is a smart guy, and choosing to fight the Ice Wyvern was, in fact, a good decision.
First of all, due to the wyvern's highly cautious nature, it takes time before it even makes its first attack. This means they'll rack up free points just by selecting this creature as their opponent.
Second, Alucio's mana attribute is fire, which directly counters the wyvern's ice-based attacks. Fire spells are twice as effective when dealing with ice-element enemies, both offensively and defensively.
On top of that, his teammate, Flagen, also wields fire attribute mana. The third member, Minet, doesn't have fire mana, but she can still play her part. If a mage casts a spell outside their primary mana attribute, it simply becomes less effective—that's all. There's no strict restriction that a fire mage can only cast fire spells. As long as the nature of the spell doesn't conflict with the user's mana, like a fire mage trying to cast an ice spell, they can still contribute meaningfully.