English has several verb forms that can be used to talk about the past. The two that you mention is the perfect aspect "Have you met" and the past tense (or preterite tense) "Did you meet".
Without further context, both would be acceptable ways to ask a question about a past event (meeting the boss).
There are a couple of differences. Firstly dialect. Everything else being equal, Americans tend to prefer the past tense. British speakers are more likely to use the perfect. This is why you perceive many people using "did"; you are talking to Americans.
There are nuanced differences in meaning. The past tense form has an implied time in the past. If you add an explicit time phrase, you must use the past tense "Did you meet the boss yesterday?"
In the cousins example, there is an implied time of "while you were on the trip" Hence "Did you meet them" is more likely.
The perfect form has an implied connection to the present. There is a lot implied about meeting a boss. Why is the co-worker meeting with the boss? Is there something that the co-worker wants from the boss, or vice-versa? If does the co-worker have the thing that they want. That is a connection with the present, and would make "Have you met" a more likely question.