Did you win? is asking about the past. It is the past tense of do. Rearranging the words yields you did win, which is, essentially, you won. There is no need for a double of the past tense (you did won).
You just won is the same as the above, with the simple addition of a slight modifier, just.
Did you just win a camera? Rearranging the words: You did just win a camera = (remember, there is no need for a double past tense) you just won a camera.
Did you just won is two simple past tenses. There is no construction with did such as this in English. The correct construction is in the bold above.
I sympathize with the heartfelt cry, "Does the English language not specify which tense that we must use when sentences are constructed like this?" The answer is sort of. "The English language" is really the speakers of the English language, and they don't always agree with each other, and they're not always consistent, especially in informal communication like the spoken dialog that you're reporting.
The first case you cite is, I think, the result of reported speech (or in this case, thinking.) If Mr. Bruce were reporting his thoughts directly, he would have told the narrator: I thought, "I will tell you when I see you." But Mr. Bruce tells the narrator a report of this thinking: I though I'd [I would] tell you when I saw you." This is called "backshifting the tense" for a past report ("thought"), and it takes "will" to "would," and "see" to "saw."
The second case has almost the same structure, but with a slight syntactic ambiguity about the reported thought. Is it of
"I will tell you."
or is it of
"I will tell you before you get to the office."
In the latter case, "get" should be backshifted to got. In the former, the temporal clause is not part of the report, and the verb "get" is in the present, which is used for near-future events.
Of course, that future sense clashes with the past "I thought," but getting the tenses technically correct would require something like, "Before you get to work, I will have thought that I had told you," and no one would say that.
There also is some sense of obligation in the sentence, not only that the speaker would warn the narrator but that he should. In which case, the sentence "I thought I should tell you before you get to work" is fine with the present tense indicating an ongoing situation.
Remember that it's dialog, and people don't always speak "correctly." Perhaps the author deliberately tried to mimic everyday speech, or perhaps he got it "wrong" in the first place.
Best Answer
There's a handy explanation of this here, but the salient takeaway point is that present participles do not determine tense.
In these passages, the present participle is determining the form, which points out that the subject was performing that action during the past action specified: in the first case, while the BFG was hurrying into the cave, he had Sophie sitting on his hand.
Here are another couple of helpful paragraphs from the link above:
In conclusion, the sentence in your story is perfectly fine.