All organic matter, such as wood, dried leaves, peat, will leech tannins into the water. But the level depends upon the quantity of the substance and does obviously dissipate over time. Wood for example tends to release tannins more during the first couple of months, then hardly noticeable at all. Dried leaves can be heavy with tannin release, and they are fairly easy to replace--at least for me, here in a northern temperate climate where I can collect bags of dead fallen oak leaves every autumn from the back garden and replace them in the tank every couple of weeks. In my 10g tank used to spawn and rear fry, the water is quite yellowish brown from the leaves. Peat is good for heavy tannins, initially, but it wears out.
You can buy "blackwater" additives. Now, I am not a fan of using any additives unless absolutely necessary, but a blackwater additive I would think would be less concern for fish if it is made from natural substances. Tannins have no detriment to soft water fish. Aside from the tint to the water, other beneficial bacteria will be present.