This (as opposed to a couple of other) usage of ては is, to my mind, just an emphatic use of て form. Importantly, however, it is used where the outcome – or the subjective comment on the outcome – is negative. A little more specifically, in a sentence Aては、B, A expresses the action or state for which the following negative statement B applies.
You sound a little confused about the similar and different usages of 'if', 'when', and 'because' in English... but I would say that you've almost certainly confronted this problem before, when translating たら from Japanese to English. So perhaps thinking about when you translate たら as 'if' vs 'when' will help you to understand this use of ては.
Other example usages of this ては are:
- When I'm this busy, I can't even read the newspaper.
- If I'm forced to work like this, I will end up becoming ill.
- If he comes, he'll get in the way.
(taken from Makino & Tsutsui's 'A Dictionary of Intermediate Japanese Grammar')
Hope that helps!
(I would, as an aside, suggest you find another resource to complement Nihongo Sou Matome, as it (clearly!) lacks sufficient (or any) explanation of the grammar points. It's not nearly enough to just have the translation, especially when their translations are often awkward in English, and occasionally just simply incorrect. Best of luck!)