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In this paper, by extending some <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>L</mi><mi>p</mi></msup></semantics></math></inline-formula>-norm inequalities to similar inequalities for Orlicz space (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>L</mi><mi mathvariant="sans-serif">Φ</mi></msup></semantics></math></inline-formula>-norm), we provide equivalent conditions for composition operators to have the shadowing property on the Orlicz space <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mi>L</mi><mi mathvariant="sans-serif">Φ</mi></msup><mrow><mo>(</mo><mi>μ</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula>. Additionally, we show that for composition operators on Orlicz spaces, the concepts of generalized hyperbolicity and the shadowing property are equivalent. These results extend similar findings on <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>L</mi><mi>p</mi></msup></semantics></math></inline-formula>-spaces to Orlicz spaces.