FoundationDB provides real ACID transactions and external consistency, and definitely does NOT rely on clock accuracy for soundness! (Google Spanner, which we are often compared to, does use a trusted clock, but Google went to extreme measures to make it accurate, including installing atomic clocks and GPS hardware.)
As for how, it's a long story. At bottom we rely on Paxos for consistency across failures, but we only actually do Paxos when there are failures. (We use less costly synchronous techniques for replication in "happy times".)