Typing Hangul is just like typing Latin, Greek, Cyrillic, Hebrew, Arabic, etc., text: one alphabetic unit at a time. The only thing a Hangul IME does is it groups the typed jamo into syllables. The grouping is unambiguous, so there's no need for popups or space presses to guide the grouping.
(If there had been the kind of rendering technology that is used for Indic text today back when Korean text processing on computers started, chances are that the syllable grouping would be handled as rendering-time shaping and not as an input-time IME issue.)
Additionally, Korean IMEs have a feature to convert a word into Hanja, but it's something you need to take action to invoke as opposed to Japanese IMEs offering to convert to Kanji by default.