The match official yellow-carded Tornado defender Mapego Maphakane after seven minutes at Orlando Stadium and again nine minutes into the second half of the first-round tie.
But believing he had cautioned different players, Chuma did not show Maphakane a red card and allowed play to continue for six minutes before the fourth official intervened.
The referee insisted he had booked different Tornado players, but the fourth official said big-screen replays proved Maphakane was the offender on each occasion.
Out came a belated red card, Maphakane sheepishly departed, and any lingering hope Tornado from Indian Ocean town East London had of pulling off a sensational victory disappeared.
Already two goals behind, they conceded two more with 10 men and former African champions Pirates were twice denied by the woodwork.
Tornado, coached by Pirates legend Jerry Sikhosana, entered the game tentatively having suffered an eight-goal drubbing in a previous South African Cup appearance.
And fears of another mauling heightened after just seven minutes when Buccaneer Lennox Bacela converted a harshly-awarded penalty.
Thandani Ntshumayelo scored a second goal midway through the first half, slamming a cut-back over goalkeeper Sizwe Majola and into the roof of the net.
Majola should have prevented Ntshumayelo scoring with a weak shot on 72 minutes and Sifiso Myeni completed the rout three minutes from time.
Mpumalanga Black Aces took advantage of playing at home to edge Maritzburg United 2-1 in an all-Premiership tie.
Lehlohonolo Nonyane and Dino Ndlovu gave Aces a two-goal lead at Mbombela Stadium in north-eastern city Nelspruit before Ghanaian Mohammed Anas halved the deficit.
The other 14 first-round fixtures are scheduled for Friday, Saturday, Sunday and next Wednesday.