The terms can be confusing here. "Alkalinity" can mean simply a high pH, or it can refer to carbonate hardness, also known as buffering capacity.
To make things worse, "soft water" can mean a variety of things, chemically speaking. In aquarium terms, we usually say "soft" to mean that the water has a very low mineral content, but water can also have a lot of dissolved solids (minerals) and still be "soft" in the sense of sudsing readily when detergent is added. The classic example of this is water coming out of a household water softening device. Such water is low in calcium, but quite high in sodium (water softeners typically exchange sodium ions for calcium ions), so it is more or less brackish water for aquarium purposes. (As you know, common salt is sodium chloride, which breaks into sodium and chloride ions when it is dissolved in water.)
Soft water with a high pH is unusual, but quite possible. If your water is soft overall (meaning low in total dissolved minerals), I suspect that your buffering capacity is also low. In that case, it will be easy to reduce the pH. You can use any of the acid buffers sold for aquarium use. Peat moss in the filter or bogwood in the tank will also usually reduce the pH, although the pH of both peat moss and bogwood can vary considerably, depending on the source of the peat or wood. In addition, peat moss and bogwood will add tannins and humic acids to the water (staining the water brown or yellow), which is beneficial to most rain forest fish, especially those from "blackwater" habitats such as much of the Amazon Basin.
If, on the other hand, you have high alkalinity in the sense of high carbonate hardness, it will be very difficult to bring down the pH of the water and keep it down. You can add acids, but the carbonates will react with the acids to neutralize them, and the pH will soon rebound to its former level, or close to it. (That's why carbonate hardness is known as "buffering capacity." Buffering capacity is defined as resistance to a drop in pH.) Usually, a different water source, such as RO or distilled water, is the only practical solution to this problem.