until, till, soup, to soak
洎 centers on a liquid-related boundary or process: reaching a point in time (until/till) or a state of being soaked, and by extension a liquid food like soup.
洎 combines 氵 (water) with 自, which likely contributes the sound. The exact historical development of the meaning 'until' is uncertain.
Water 氵 beside 自 (oneself) suggests soaking oneself or reaching a point where water covers something, like soup filling a bowl or time reaching a limit.
For キ, imagine a key floating in a bowl of soup: key -> キ, and the soup soaks the key until it sinks.