I read that you can only tamper with a blockchain if you have more than 50% of the computing power in the network. So say you have 51% of the computing power, then you can create a longer blockchain than the legit one. But how does this one get accepted by the network? I mean, the blockchain gets extended when people broadcast the transfers they want to make. Say the 51% wants to change something 10 blocks earlier. Does he change the copy independently of the network until it's longer than the network's copy? And how does he present it to the network then? Doesn't the network see that since a certain block, all the following blocks are suddenly different from those of the previously ongoing blockchain, which the entire network considered legit?
I know the longest chain gets accepted as the legit one because it's (almost) impossible to have more than half of the computing power but can't they add some security that takes it into account if, like, all but one node have a shorter blockchain, this is probably the legit one?
My apologies if this is considered a very basic question. Just trying to understand the main concepts and can't really find a straightforward answer to this.