The people's motivations here made as much sense as the rest of the plausibility issues. I am not sure that the writer has ever met real people, and I am saying this as someone who hasn't. Everyone, including the Doctor, was syncopatic in this. First, why worry about the potential world-scale disaster brewing or fierce creatures in the forest, when we have children to get home? Then, why be impressed by a TARDIS when there are trees? And don't forget to kill all the children because they'd spend the rest of their lives crying for their parents. And look, I have been a soldier, I don't need to see solar flares. Wow.
Besides, Clara suggested that the TARDIS – which like a big brother of Rhode Island, could easily fit all of humanity inside of itself – could serve as a life boat. It can also time travel so it can collect all of humanity in a jiffy. It has previously moved an entire planet – Gallifrey – to a different reality, and the Doctor cares for Earth just as much (if not more). Clara happens to know all of that. There's no way to explain the whole let us burn, go save yourself, we have to get the children home. What?! WHAAT!? Seriously, WHAT?