Vowel harmony comes in two types: unidirectional and bidirectional. With bidirectional harmony, some syllable in a word has the "dominant" value, and everything else in the domain gets that value. Nilotic ATR harmony is a typical example. Otherwise, a certain edge of the word predominates, for instance the vowel quality (frontness) of the whole word in Finnish is determined by the first vowel, so the rule operates from left to right. The rule can also operate from right to left. However, the better generalization is not about first vowel versus last vowel, it's the direction that matters. Menomini vowel harmony goes from right to left, but it doesn't necessarily start with the last vowel, it starts with any high vowel (it raises certain preceding vowels). Some Romance language have stress-based limits where harmony only goes from the end of the word to the stressed syllable.
There are many factors that are relevant to harmony, for example some consonants are irrelevant and some are relevant; sometimes only certain vowels are targetted or trigger the process. van der Hulst (2019) Asymmetries in Vowel Harmony gives an overview, and in a couple of years a massive collection of studies edited by van der Hulst & Ritter will become available.