Welcome to the forum.
Not a good note to start on.
Has something changed after the patch ?
I patched to (1.02 ) almost immediately i got Trop2. So I didnt notice any difference around the log/captain issue you have highlighted.
Ive assumed that the Anne Bonny pirate king ive selected in my sandbox game has no bearing on the initial Captain who starts on my island. Like you its always been Morgan.
Would make more sense to have the Captain match with the island King/queen.
Below is a brand new sandbox..and yep... Anne Bonny selected yet with Morgan on the island.