Are you talking about extractions? If so, I'm not sure if it matters whether you add acid or base first, but you have to add the weak acid or base before the strong. This is because some compunds may be extracted in weak acids or bases and be separated, while other might require strong acids or bases. If yo add the strong acid/base first, both types of compunds will come out and you won't be able to separate the weaker ones.
If anyone could comment on whether acid or base first matters, I'd like to know too!