Hi.
In my opinion it may not be black spot disease since this is a tropical tree and they are not prone to this type of disease.
I strongly suggest to check underneath the leaves that are turning yellow and check for mites.
Do the leaves feel sticky?
I don't remember the leaves feeling sticky. I sprayed with some Neem oil and the problem went away. Then, I left for a couple of days for vacation, left my new watering system with misters on and came back to bugs.
Little bugs, which I assume were aphids were inside the soil. I could move a bit of the soil aside and see the bugs moving about. The leaves looked like they had been chewed on as well. I used Malathion on the soil and the leaves, that got rid of the little critters right away. Now, it's starting to recover a bit. The pads are starting to fill in.
I've got to do some work on clearing out the pads, getting rid of some of the "unwanted" branches, but that will come later. I really think I need it to just strengthen a bit.
Here's the tree this morning: