Does the Active Azerite Power Trait 'Filthy Transfusion' deal AoE damage?

One of the new Azerite traits in World of Warcraft is Filthy Transfusion, which "Your damaging abilities have a chance to invoke a tainted swamp beneath the target, siphoning 3654 health from them over 6 sec."

If other monsters are standing in the pool, will it deal damage to them as well?

It's a single target skill.

With two or more targets it siphons health from the one with the debuff. You can however try to apply the spell on more than one target (depending on your haste value you may get enough procs).

Also Blizzard would have written the tooltip differently if it was an AoE skill. They used to write "nearby" or "any/all/x enemies" on AoE tooltips (pretty much like for the Azerite Globules).