I don't know for a fact, but it seems to me that the ports do their own scheduling. I say this because I have seen instances where a ship arriving later than scheduled didn't have a place to dock.
On the more common runs with repeating schedules, ie: Oasis and common ports like St Thomas, the agreement is between the port and the cruise line. St Thomas had to undergo a six-month dredging process to accomodate Oasis.
Now that it is common knowledge Oasis will be there it is up to other cruise lines as to whether they also want to go there.
But I also have to say I think you blowing Oasis out of proportion. St Thomas regularly has four or five ships in port, many of them carrying over 3000 passengers. Oasis is equal to 1 1/2 ships, maybe two, in terms of what it carries. So, if you have five ships in St Thomas, or four, one of them being Oasis, there isn't much difference.
You make it sound like Oasis landing anywhere is going to creat chaos. In reality, the number of passenger visits to St Thomas will not be affected so much on a percentage basis by Oasis as much as other factors (like the overall growth in cruise ship capacity) will affect it.