The 26-year-old moved from WA for this season after being unable to break into their Shield line-up.
Jackson lost his contract despite being WA's leading wicket-taker in domestic one-dayers and also playing for Australia A last year in a Top End series against Sri Lanka A.
But he shone in his debut on Thursday in the Shield season-opening game in Sydney as the Tasmanians blew a strong start.
Jackson took 3-36 and Jake Scott snared 4-35 as Tasmania reached 9-241 stumps at Cricket Central after NSW won the toss.
Ben McDermott brought up 3500 Shield runs with his 77, and opener Caleb Jewell made 50.
After Jackson had Tasmanian captain Jordan Silk caught behind for five - his maiden Shield wicket - Jewell and No.3 Tim Ward put on 93 for the second wicket.
But Jewell slashed at Scott and was caught by NSW captain Charlie Stobo.
That sparked a collapse of 4-5 that left the visitors on the brink at 5-108, with Teague Wyllie and Jake Doran both out for ducks.Â
McDermott, batting at No.5, worked with the tailenders to steady the innings, but he was the last wicket to fall for the day when Stobo took a sharp chance at gully off Scott.
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