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No, you summon your phoenix, and then, when the opponent summons theirs, the elemental balance triggers, and a phoenix with the same health and damage as the opponent's appears on your side. The attack and defense still depend on your hero, and your phoenix disappears.
But if your opponent summons a phoenix first, and a similar one appears on your side as a result of the elemental balance, and then you summon yours, the phoenix that appeared as a result of the elemental balance will disappear.
P.S. Sorry for the poor writing.
Added after 1 hour 1 minute
Perhaps it would be good to combine the advantages of Wing and Dire Ely, Dire Ely with elementals, and BDP can be used as a hit-and-run unit, while Wing will calmly prepare for the final.