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From 《金瓶梅词话》 chapter 1 (Ming-dynasty): 这人不甚读书，终日闲游浪荡，一自父母亡后，分外不务正业 — after his parents died, the protagonist read little, drifted around, and 'particularly did not attend to his proper occupation.' The idiom has been a standard reproach ever since.
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Critical, often from parents, teachers, or commentators. Modern internet culture sometimes uses it jokingly for celebrities who dabble outside their main field (a singer who makes perfume, an actor who writes poems) — keep the tone light in that context.
