Apply the caulk after all the grouting is done and all the tiles are dry. Do not forget to leave the expansion joints free of grout. Whereas grout will harden (defeating the purpose of inserting expansion joints), the sealing compound squirted out of a caulking gun will remain flexible.
You may be familiar with caulking guns if you are accustomed to caulking around windows to make them more air-tight, as part of the process of winterizing a home. Caulking guns are used in a similar fashion in the outdoor tile patio project, except that it is water, rather than air, that you are trying to keep out.