It's more like "being accompanied by". The solvent goes around the beans and collects the caffeine as it passes each bean. When the solvent leaves the bean, it has become solvent and caffeine.
I think that the caffeine from the decaffeination process is sold as a by-product, so it's a result.
The purpose of decaffeination is to get tea/coffee with no caffeine, not to produce caffeine.

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