Pushing for a Test return, Konstas looked shocked and raised his right hand to Tasmanian umpire Michael Graham-Smith, when given out caught behind as NSW struggled to 8-174 at stumps on day two in reply to Tasmania's 427.
Playing his first game back from injury this season, Bird, 39, reduced NSW to 3-26, claiming Konstas (5), Ollie Davies (13) and Nic Maddinson (2) with exceptional swing and seam bowling. The former Test paceman finished the day with 4-39 from 15 overs.
Maddinson, the NSW Shield captain, had just returned from South Africa, where he was a shock selection at the top of the order, managing just 56 runs from four innings including two ducks. He lasted only five balls on Saturday batting at No.4, edging low to Mitch Owen at third slip.
Kurtis Patterson, who was also looking for a Test recall after making a half-century and century in his opening two Shield matches, went for 14, caught behind down the leg side hooking at a short ball from Brad Hope.
Konstas appeared to play and miss at a delivery from Jackson which moved away late. He was looking down marking his guard when Graham-Smith upheld Tasmania's appeal and took some time to leave the crease, constantly looking back at the umpire.
The 21-year-old, who played the most recent of his five Tests in the West Indies last year, had started this season brilliantly.
After touring India with Australia A, he scored 71 and 151 not out in a recent Sheffield Shield match against Western Australia at the WACA. He then made it two centuries in four days after compiling a brisk 149 in a one-day game against the West Australians.
NSW lost wickets regularly, with Lachlan Shaw (45) becoming Bird's fourth victim. Jack Scott made 31 and Ryan Hicks 43 mounted a minor recovery.
Tasmania had resumed at 5-335, adding a further 92 to their overnight score.
Brad Hope missed out on his century when caught by Ryan Hicks off the bowling of Ben Dwarshuis for 99, while Jake Doran added 77.
Dwarshuis was the pick of the bowlers, finishing with 4-85.Â
