A saucer is not needed; if there is one under the pot, remove it.
Only water the plant when the pots feel light weighted. Just lift one side of the pot once it’s dry and do the same once you water the plant. You get the idea of when you need to water your pot. I would also cut two pieces of 2 by 4 (10 inches long) and place your pot on top of that. It allows for water to drain better and roots can receive some oxygen through the holes, instead of placing it directly on the ground.
Vascular veins in a leaf contains Xylem and Phloem, they transfer water and nutrients to the leaf cells. When over watered the cells in Xylem will burst and die. That is why leaves turn dark/black around the middle/edges of the leaves. Once the plant is over watered and cells have transferred all the water to the leaf you will notice that the center vein and around it will turn light green, after a day or two it will turn black or darken in color. That indicates the death of those water-carrying cells.
Also over watering any plant kept in a container (not just figs), will cause the roots to rot.
Pine bark mulch is mixed in the soil that you are preparing (with limestone and slow release fertilizer) to aid with better drainage. Since you have already up-potted your tree last month, I would not suggest taking the plant out of the pot and mixing in pine bark mulch. Just remember next time when you purchase a fig tree or any other tree that is going to be kept in a pot, add some pine bark mulch or coarse perlite to your medium.
As far as MG potting soil, either Organic or non-organic, I would hesitate to use them in future. Once the MG potting soil gets wet it becomes very dense, simply it containers too much peat moss and retain the water for a prolong time. It also contains Gnats and their larvae.
That’s why many forum members (including me) we all use other brands such as, Fertilome UPM, Farfad mix or other very light weighted mixes. They cost more but its worth it. If you can get Fertilome UPM or any professional brand of potting soil get them and use them in future. You can also use them for rooting cuttings.
And since your soil (MG) does absorb and retain water for longer periods, watered it or when the 1 inches of the soil (from top) dry out or the pots feels light weighted.
Those blackened leaves will eventually dry up and drop. Your plant will replace them again with new leaves.