The automatic compilation that you are seeing with pdflatex is likely because you have set your default compilation engine to be pdflatemk. The regular pdflatex engine doesn't do multiple combinations automatically. But there are mk versions for all three engines, and you can select them by using a "magic comment" in the first line of your document. You can type these lines yourself, or you can use the Macros->Program menu item to select from the list which will insert the relevant magic comment for you.
For automatic pdflatex compilation:
% !TEX TS-program = pdfLaTeXmk
For automatic xelatex compilation:
% !TEX TS-program = XeLaTexmk
For automatic lualatex compilation:
% !TEX TS-program = LuaLaTeXmk
If these don't work for you, you may need to move the relevant Engines from the Inactive/Latexmk folder to the main Engines folder inside your ~/Library/TeXShop folder, which you can navigate to from within TeXShop from the TeXShop menu item.
For more information on magic comments, see: