Miners don't do it, it's a user-end part that such users who are either involved in mining with a mining pool or have an account there, are given privileges to perform acceleration. IMHO, they don't do anything except re-broadcasting the transaction to the whole network, but this time, it gets added to the list of transactions that are waiting to be confirmed (the list that these miners or mining pool decide based on fee/byte). Once that pool decides to consider that fee slab, they take limited transactions in the block based on waiting queue (according to the time the transactions were done, and not the time they were accelerated).
There are many including, but not limited to, ViaBTC, BTC.com, Antpool, etc. But that doesn't really guarantee that it will "officially" be taken into a block unless you have your own pool and/or a lot of hashrate to decide which fee slabs to be included.