Yu-Gi-Oh Tribute effect
No you would not get the effect if you used the stated monster as a tribute for something else.

The text states: 


  "tribute this monster to"


this means tributing this card is a cost to activate the effect to destroy a face up card on the field.

if it read:


  When/If this monster is tributed 


then it would work when you used it for a tribute summon or any effect that caused it to be tributed