When an Englishman described the soil in a pot around the feet of his plants or trees, s/he often says 'compost' as a generic and global term.
Often when an USain says compost, s/he means the stuff of a compost bin.
Very often 'organic' and 'compost' get muddled and transposed.
I believe the original question had this topic correct, that of 'organic' means any
once living material in a soil mixture.
The problem pops up that trees need very fast draining soil with a high percent of air in the mix. Soil with very small particle size, like loess or peat don't outgas well. making anoxic soil that drowns woody plants in tiny pots.
If you spend much time rummaging around at bonsai sites looking at photos, you will at times see trees in their pots wedged up at an angle. This is to improve drainage of the soil in those pots.
Its only in the tropics that you will see bonsai soil with higher amounts of peat or sphagnum in their soil mix. So if your growing in San Juan, get your soil training locally...