Well Sharingan has the ability to sense chakra, not as accurately as Byakugan but still able to. How else does sharingan copy jutsu? They must have some idea of how the chakra will flow. If that is true then a mine full of explosive chakra would be like a glowing beacon to Sharingan and Byakugan. Sasuke probably saw a faint glow in the ground and threw a sword at it just to make sure.
Also, Tobi could easily of learned Deidra's techniques just by the 2 talking, he doesn't have to demonstrate it for him to know. Also if that Tobi indeed is Uchiha Madara then his Sharingan could have read Deidra's mind, he probably knows every jutsu of every akatsuki member.