On a newly planted tree like that with a rootball, you need to water just like you would before it was moved. The roots haven't extended into the new soil yet. You need to keep the rootball moist until new roots form. That will take weeks.

Right now the old rootball is probably dried out and all that new moist soil isn't helping yet.

One sixteenth inch holes are not big enough. Look at the holes in commercial pots. They are at least one half inch in much smaller pots like 12". As an example, I have 6 one inch holes in a half whiskey barrel which had worked well for several years. Also, even though you transplanted the fig with the root ball intact, it may be suffering transplant shock. I find the figs' leaves yellow and drop when they do not get enough water as fruitnut suggested.

Cath