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Can someone give a comprehensive explanation for this?

Doesn't current account include international income and transfers?
2. +if the current account gets smaller, it means that less is being imported and more is being exported, which means more is injected into the economy/circular flow, which increases AD. think of the formula of AD ( AD = C+I+G+(X-M)), if the value of one of C or I or G or (X-M) increases, then ad would increase and shift right.

tl;dr if current account is smaller this means less imports and more exports, so (x-m) is bigger and therefore ad value increases and therefore shifts right
don't forget about the equation of AD=C+I+G+(X-M) , always write it down when you have a question on it and which ever of the values of the equation increases or decreases, ad increases or decreases

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