Eddy the mage is facing 3 Azors, which are 15, 25 and 10 ft far away from him. Azors have the special trait Heated Body (emphasis mine):
Heated Body. A creature that touches the azer or hits it with a melee attack while within 5 feet of it takes 5 (1d10) fire damage.
Eddy casts Steel Wind Strike (emphasis mine):
You flourish the weapon used in the casting and then vanish to strike like the wind. Choose up to five creatures you can see within range. Make a melee spell attack against each target. On a hit, a target takes 6d10 force damage.
You can then teleport to an unoccupied space you can see within 5 feet of one of the targets you hit or missed.
hits all of them, and he does not teleport from his current position.
Since a melee spell attack is a melee attack, does Eddy take the fire damage given by the Heated Body trait? Is he considered to be within 5 feet during each attack?