What about the diet of the tarsier is different from that of all other primates ?

Tarsiers live exclusively on animal prey. Their diet includes primarily insects such as cockroaches and crickets, but may occasionally be extended with reptiles, birds, and bats. A Philippine tarsier in captivity will eat live shrimp and fish in a bowl of water.

Also: Folk traditions sometimes has it that tarsiers eat charcoal, but actually they retrieve the insects from (sometimes burned) wood.

Quite right.

Thanks for the answer and Happy Friday mozart56 !