That power's mechanical description is not totally clear.
Effect: You may fire at as many enemies in burst as you have bullets left in your guns. If you reload, this attack ends.
This effect line is fairly clear: if you have five bullets left in your gun, you can fire on five enemies. However, the Attack line says this:
Attack: Dexterity - 1 vs. AC, eight attacks
The "eight attacks" part suggests you get to attack eight times - regardless of how many bullets are left in your gun. Those attacks have to involve firing your guns because the effect line - which has mechanical weight - states this attack is performed by firing at the enemies.
Those two lines in combination suggest that if you have three bullets in your gun, you can target up to three enemies and distribute your eight attacks between them.
But wait! If you reload, the power ends! You can only take three shots, right? Sure, that's true. You might imagine this means you have to stop after three attacks, but in 4e, simulation and realism don't matter. The mechanics work the way they say, sense and realism be damned, and it's up to you to work out how stuff makes sense. The mechanics never say you use one bullet per attack. They do however say you could potentially be making eight attacks against one creature with one bullet. Maybe the bullet ricochets a few times, or it's one super-effective shot.
This power is poorly expressed, in part because the author appears to have misunderstood the purpose and full utility of the effect, target and hit lines.
Talk with your group about it and rewrite the power so it works the way your group (and the player of the Gunslinger!) agrees it should work. Or consider not using this homebrew Gunslinger, and pick a ranged character to refluff instead. Don't take this for an expression of dislike for homebrew in general: this homebrew in particular, however, seems to have ineffectively written powers, though, so tread with caution.