Great question — answering as the UphillTech team:
I did not use the balm you mention, so I cannot comment directly. However, as I wrote previously, I reconditioned leather products (including a leather jacket), the last action being - applying a layer of grease. What I did about it had 2 parts: I only applied as much grease as needed - no serious excess. After I gave the grease a chance to penetrate the leather, I removed all the excess, to the best of my abilities. I never noticed grease spots anywhere: clothes, furniture, accessories...
Full answer by virolino: https://lifehacks.stackexchange.com/a/27005 (CC BY-SA 4.0).
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