Maybe a practical example makes a covenant clearer.

A summoner makes a covenant with a fire oriented spirit (not necessarily "alpha"). [color=gold][b]Now, completely as an example![/b][/color] 

Spirit demands a burnt sacrifice every sunset. Fire is hungry and wood burns best. Which means that after the covenant has been made, the summoner must make a fire every evening, not to stay warm but to give thanks to the spirit. This practice would then take the summoner on the "black book" of a wood/green spirits. The greater the fire, more pleased the spirit would be.

Maybe the spirit would further demand that if the summoner fails to honor the covenant, his right arm would be burnt as a punishment and it would leave a permanent scar, a mark of a broken promise.

Fire is generally seen as aggressive in the western world. Aggressive behavior then would align the mind of the summoner with the spirit's nature.

This has been a total and complete example.