Dark circles around eyes may be of many reasons.
1.Atopy (Allergy)
2.Familial
3.Inadequate Sleep (qty and Quality)
4.Constipation or Bowel Problem.
I think it is not related to the hot water compression.
Check if you have any.
PLEASE DON'T APPLY ANY SKIN CREAM AROUND EYES BECAUSE MOST PRODUCTS CONTAIN STEROIDS TO LIGHTEN.IT CAN CAUSE INCREASE IN IOP, STEROID INDUCED GLAUCOMA IN SUSCEPTIBLE INDIVIDUALS.
Next Steps
If the tip doesn't work consult a physician followed by a Dermatologist.
Health Tips
Apply juice of potato around eyes daily at night which will decrease the darkening.
Apply cut cucumbers over eyes daily.
wash your face several times with cold water