A vehicle with turbo boostas can trigger them in any of its movement phases. The turbo boostas add D6" to its movement, but for shooting and disembarking troops the vehicle counts as moving at the speed it went before the turbo boosters were added. The extra D6" movement must be used to move in a straight line and if a 4+ is rolled the vehicle and any passengers onboard may not shoot or disembark that turn as they're too busy hanging on for grim death.
Errata — Chapter Approved: Codex: Orks Q&A (v1.0): Combining Turbo Boosta with a Red Paint Job does not let a vehicle move a full 13" and still count as stationary for shooting and disembarking purposes. The 4+ restriction is checked against the distance actually rolled on the turbo boost dice — if that roll comes up a 4, 5, or 6, the vehicle and passengers can't shoot or disembark, regardless of how the Red Paint Job's flat +1" then gets added on top. A vehicle could still get lucky rolling a 3" or less and combine that with the Red Paint Job's bonus while remaining eligible to shoot, but it's a real gamble, not a guaranteed loophole.