Why does Mahmut empty a bottle of liquid upon returning home?
I haven't seen the series, but it sounds like a libation, or ritual pouring of liquid.  See https://en.wikipedia.org/wiki/Libation . It is an ancient practice of many cultures, usually as an offering to a god or in remembrance of those who have passed on. If the series takes part in Japan, it may specifically be a Shinto or Buddhist practice, but if in an anonymous fantasy world, they probably generalized the custom.  What you describe certainly fits with what the article states.