If someone tampers with a transaction in an old block, how does the network detect it?

Editing any past data changes that block's hash, which breaks its link to every following block — so the tamperer would have to re-mine that block and all blocks after it, which is computationally infeasible on a large chain.

Because each block's validity depends on the previous hash, a single change ripples forward: the edited block's hash no longer meets the puzzle target, and its "previous hash" link to the next block is now wrong, invalidating the entire rest of the chain. To hide the change, an attacker would have to redo the Proof of Work for the altered block and re-mine every subsequent block to rebuild the whole chain of valid hashes — while honest miners keep extending the real chain and racing ahead. The deeper the block, the more work must be redone, so old transactions become effectively permanent. This is why people wait for block confirmations: each new block mined on top of yours is another layer of work an attacker would have to beat.

Go deeper:

• Double-spending — Wikipedia — why re-mining a buried block and every block after it becomes infeasible, and why confirmations matter.