Those interests divide into three parts: eliminating foreign powers from the region to maximize Iranian power, convincing Saudi Arabia and other countries in the region that they must reach an accommodation with Iran or face potentially dangerous consequences, and a redefinition of the economics of oil in the Persian Gulf in favor of Iran, including Iranian participation in oil projects in other Persian Gulf countries and regional investment in Iranian energy development.
Whether Iran caused the rising in the first place is unclear and unimportant; it is certainly involved now, as are the Saudis.