Punctured phone battery
Wait a week and dispose of the battery at your locally hazardous waste disposal center.

A swollen battery pouch contains gasses due to aging or overloading. This is a stable state. Although continuing to use the battery is not recommended.
An opened battery pouch allows oxygen to enter, which may cause a mild exothermic reaction. As in, it becomes a bit warm and may smoke or smoulder.
A punctured battery (as in, straight trough with a nail or knife) often causes a short circuit in the battery layers, which causes very high current, the electrolyte to evaporate very fast, the pouch to burst open, and since it was very hot, combustion of the evaporated electrolyte and often also ignition of the lithium cobalt-oxide. (aka a battery fire)

The electrolyte and the fumes are toxic, do no breathe.
Water is a safe method to prevent flames or cool a pack to prevent triggering other cells in thermal runaway, which is melting of the polymers between electrodes causing a short circuit again, see above.
Especially with small batteries submerging them completely contains the risk to a small area and prevents flames.
Water will not cause an alkali reaction everyone is afraid of. This only happens with non-rechargable lithium batteries.
The black residue you see is the lithium cobalt oxide.


Bonus slow motion x-ray footage of battery puntcture.