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:
Any Usage Works
By the same token, the other usages of present participles are perfectly appropriate in past-tense narratives. In non-finite clauses, present participles are verbs in a dependent clause that joins to an independent clause: "Sitting alone, I am perfectly content." Change the main verb, and it's just as easily past tense: "Sitting alone, I was perfectly content." Even used as nouns or adjectives, they are appropriate in past tense: "That was good thinking on her part" and "The sinking sun was beautiful."
Present Participles Work Anywhere
A writer can successfully use present participles in past-tense narratives, as long as he remembers that the word "present" in the "present participle" is its form, not its tense. A present-tense sentence that uses a present participle becomes the past tense through the main verb of the sentence, not through the participle that accompanies it as auxiliary verb, verb-into-noun or modifier.
In conclusion, the sentence in your story is perfectly fine.