I upvoted @BrianHooper's answer, because I believe top-down and bottom-up are the terms used in a constructive context (I've seen it in software engineering, but also in the context of a marketing strategy, portfolio construction, and of building out a business).
But for the sake of having a variety of answers, and in case you come across a need to express these concepts in different contexts, here's a couple more sets of terms.
Scientific endeavors will often have a period of analysis (breaking down observations into their constituent elements) followed by a period of synthesis (identification of patterns found among those primitive elements).
Similarly, philosophers will often debate the relative merits and legitimacy of deductive (top-down) and inductive (bottom-up) reasoning.
Side note: weaker counterparts to these types of reasoning exist: abductive is deductive reasoning using facts known to be imperfect or incomplete (a "best guess", e.g. a medical diagnosis); conductive is inductive reasoning using supporting arguments (because you don't think the facts necessarily speak for themselves).
For these reasons, if you want to say "X is philosophically committed to taking a bottom-up approach", you might say "X is an inductionist" (or subscribes to inductionism). Similarly, if you want to say "X understands how things work by taking them apart", you might say "X is an analyst". Unfortunately, inductivist and deductivist are really only applicable to certain stances in the philosophy of science (note the suffix, -iVist, compared the the -iONist of inductionist; a subtle distinction that makes a big difference).