The pool manager is in charge of validating transactions and building a candidate block for the pool miners :
Most mining pools are "managed," meaning that there is a company or individual running a pool server. The owner of the pool server is called the pool operator, and he charges pool miners a percentage fee of the earnings.
The pool server runs specialized software and a pool-mining protocol that coordinate the activities of the pool miners. The pool server is also connected to one or more full bitcoin nodes and has direct access to a full copy of the blockchain database. This allows the pool server to validate blocks and transactions on behalf of the pool miners, relieving them of the burden of running a full node.
Miners are thus only involved in the resolution of the PoW algorithm by providing computing power to the pool :
The pool server constructs a candidate block by aggregating transactions, adding a coinbase transaction (with extra nonce space), calculating the merkle root, and linking to the previous block hash. The header of the candidate block is then sent to each of the pool miners as a template. Each pool miner then mines using the block template, at a higher (easier) target than the bitcoin network target, and sends any successful results back to the pool server to earn shares.
The sources come from the book Mastering Bitcoin, chapter 10 about mining and consensus, that I strongly recommend you for more information on the subject : https://github.com/bitcoinbook/bitcoinbook/blob/develop/ch10.asciidoc.
Of course this can be extended to Ethereum mining pools.