I don't believe so. They are using a lot of ethereum design, I think, but not actually running on ethereum:

Tempo blocks extend the Ethereum block format in multiple ways: there are new header fields to account for payment lanes and shared gas accounting, and system transactions are added to the block body for the fee AMM and other protocol operations. This specification contains all the modifications to the block format. protocol overview

Interestingly, I found this about running a "validator node":

https://docs.tempo.xyz/guide/node/validator