In so far as Pearl has a theory of causation, it is a manipulability theory. Sure, Pearl provides a method for drawing causal conclusions from data about correlations. But what he means by causation is cashed out in terms of how interventions on one variable affect another variable, not just in terms of correlations. Correlations are indicators of causation for Pearl, but they don't constitute causation. The structural equations Pearl uses to represent causal relationships are meant to capture not just de facto mathematical relations between variables, they support counterfactuals. They tell us what would happen to the variable on the left hand side of the equation if the variables on the right hand side were manipulated.

See section 6 of the SEP article for connections between the manipulability theory of causation and Pearl's formalism.