Why doesn't this mean "I work here during the summer"?
And if it's going to use "since", it needs to use the present perfect, not the simple present. "I have worked here since the summer"
In another example was traslated as "during". What's the difference?
Is that an accepted wrong answer or are you suggesting it should be the only correct one?
Yes, it should be: I work here during the summer, or I have worked here since the beginning of the summer (or since last summer).