Regardless of when you are drafted, you should make steady progress. A high pick, regardless of age, should see some time in AA by the end of his 2nd year of pro ball, and first rounders are usually expected to be decent enough to qualify for a September call-up after 2 years and not later than 3 years.
That's pretty aggressive. If a high schooler is in rookie ball (NY-Penn) his second year, that's not too slow. At the start of this year, I think there were 2 19 year olds in the Carolina league - Moustakas and I forget. There were 7 same age as Marrero (20, turning 21 during the seaosn). 22 in AA is not that old. League average age for the Eastern League at the start of the year was 24+.
[edit - Moustakas is 2 months younger than Marrero. he was 20 in April]