It is important to correct the drainage. The soil looks like it has a lot of fine sand in it, almost like the natural soil in your area. Fine sand like this resists taking up water when it is very dry, but when finally wet it holds too much water and not enough oxygen. Eventually you will need to remove as much of the old soil as possible, but not at the first re-pot.
Don't agonize over the new soil. Almost anything with larger particles will work, about 1/8" in diameter. A cactus mix from a big box store would probably be okay. You likely will re-pot this tree every year for the first few years, so you don't need expensive bonsai soil right now.
You can probably tell I really like dwarf schefflera, LOL. I have five in various stages, the first one started as an over-grown house plant. They work as bonsai in only a few styles, mostly clump, multi-trunk, or banyan. Wire doesn't work well on them, so they are developed primarily by grow-and-clip. Here is a photo of one by Jim Smith at the Heathcote Botanical Gardens in Fort Pierce. The bonsai collection there is very good, and they are all species that grow well in your climate.
