Yeah.
Hmm.
I wonder when Admirals get their DFs. During Marine traning or right before ranking up to Admiral.
I think the first one.
I think they just randomly come across it in most cases. Like, Borsalino killed a pirate who had the Pika Pika fruit. Or maybe the Marines give powerful logias to certain Marines who they think have potential.
Maybe Kuzan got his from Garp or Sengoku, but he had it as a vice admiral too. So did Borsalino I think.
In Issho's case, he probably got it shortly before becoming an admiral. Aramaki hasn't eaten in 3 years, so I figure he's had his for ages.