Britain was exporting oil from Iran, which was understood and agreed on.

Russia was trying to turn Iran communist, so it spread the message that Britain was taking advantage of Iran's oil and stealing the country blind in order to help overthrow the government.

The Islamic revolutionaries and the communists helped overthrow the government.

Then the Islamic revolutionaries executed the communists after they complained that they weren't being given an opportunity to help administer the country.

The Islamic revolutionaries were basically chanting "neither east, nor west". No capitalism taking advantage of Iran's resources, no Russian communists taking control of their government.

From there, the revolution now had a state and it could leverage the state's resources to export and fund its revolution to other countries which it has done extensively.