High draft picks always get their playing time, especially when they are considered a "generational talent".
Overall, yes, players selected with the first picks in the draft typically receive a lot of minutes in their debut season, but that's not always the case. Take, for example, Kwame Brown, Anthony Bennett, and Markelle Fultz, who were selected with the first draft picks, but in their debut season, they got few minutes and their performances were very poor, which isn't typical for players selected with the first pick in the draft.
Well many thought before that they could be a big deal on the team draft them but they didn't meet the expectation not only with their fans but also on the teams drafter them. That's why they don't get much minutes despite of their position on the draft. Majority of them are now been eliminated on the league and their career is just a short stints on NBA.
There are also a draft steal since there are drafted far like Jokic and other more became a star on their team. So overall you are right with it depends on the performance since teams would provably look at the way how player contribute. If they play good and blend well on their team then provably that they get more minutes or even receive a star status especially if he proves that he can dominate on both ends.