Pooran will now miss the next four T20I games for the Windies and will have five demerit points added to his record.
Warner was handed a suspension for being a part of the group that altered the ball with sandpaper during a Test match against South Africa in March 2018.
Smith rose above taunts of "We saw you cry on the telly" with centuries in each innings before England crumbled to a 251-run defeat.
Smith smashed a heroic 144 that not only bailed Australia out of trouble in the first Ashes 2019 Test at Edgbaston, but also helped set a competitive total.
Despite being in good nick, Warner understands that in English conditions with the ball swinging, he has to be mindful of the moving delivery.
Bancroft will almost certainly experience more of the same given he was the one who actually applied sandpaper to the ball during a Test away to South Africa.
Cummins though made it clear that the change in approach has not blunted Australia's competitiveness.
A bitter series also saw du Plessis leave the changing room at Durban's Kingsmead to witness a stairwell row between Warner and South Africa's Quinton de Kock.
To negate the threat of a hostile reception from England fans, Smith has also taken up the guitar and has been practicing on Australia's team bus during their road trips.
England cricketers going back several generations might be surprised at Lyon's characterisation, particularly given the heckling that takes place in Australia.