Hiring occurs in waves and is dictated by a waiting list. Do your CP, and about a month before your departure date you can visit casting to put your name on the FT list. Your name stays on the list for 6 months, then you have to add it again.
We recently hired several merch, then attractions, then food... it really goes in waves. I just did a new CM tour yesterday and we had new hires in vacation planning, merch, and attractions. We had two DPI as well, but they were internal transfers.
When it comes time to hire people (for full or part time) they will literally go down the list. Because most work in the park is run by the union, the job will not go to the most qualified, rather the next name on the list.
Lists typically start with full timers wanting to transfer, part timers wanting full time, seasonal CMs wanting full time, then external hires. The lists are constructed by seniority date. So that those who have worked for the company longer will get the first opportunities.
Exceptions to the "list" rule are opening teams and Entertainment. Entertainment hires based on audition scores, not on senority. Opening teams hire the best qualified, but if skills are considered equal then senority makes that final decision.
As for PIs.... it's completely random. I was offered the opportunity to stay with my team on a TA (temporary assignment) because they had funding available. These scenarios vary a lot based on the location.