Earlier quoted context omitted.
I'd say the reliability the bank is looking for is much higher than what's acceptable for web companies (i.e. web companies are fine with eventual consistency, which would is obviously unacceptable in a banking system outside of trivial non-core features).
Why would eventual consistency be unacceptable in a banking system? In my experience people interact with social media on far shorter time scales than their banks. When they post a new Instagram photo, they expect that their friends will see it basically instantaneously. In comparison, when people use their debit card at CVS, they're not expecting anyone to log into their bank account seconds later and see the charge…
However, the buck (no pun intended) has to stop somewhere. Overdraft limits have to be consistently applied. Even that is somewhat up in the air. Take this with a grain of salt as it's second-party information, but my wife works in fraud prevention at a smaller credit union. She says that transactions are collected throughout the day and overdrafts are only applied at the end of the day to allow for bills to drain your account beyond its capacity and then payroll to land without applying overdrafts unless you're in the red afterwards. In some sense, that's even "eventual consistency" on the scale of 24 hours.
The most important thing in banks is that at the end of the day, the balance sheet, well, balances. And they limit their liability by preventing too much overdraft and applying daily limits to ATM withdrawals. I pose that general eventual consistency fits that pretty well, as long as "eventual" isn't "hours" for the most part.
A little more on eventual consistency in general as I understand it, eventual consistency systems come in many forms. In a leader/follower setup (think MySQL w/ async replication), usually "important" calls are made to the leader in a consistent fashion and changes are asynchronously replicated to the followers for general read fanout. There are a lot of different kinds of systems with different guarantees. In a dynamo-style system, writes/reads are usually done to a quorum of replicas (e.x. 2/3 replicas), and only if the read from the two replicas disagree are the values on all three replicas "repaired" via last-write-wins. Facebook has a model they call causal consistency[1] which models causal relationships (e.x. B depends on A, therefore B isn't visible until A is also replicated).
You can consider any system with a queue or log in it that doesn't provide some token to check for operation completion to be eventual. For example, imagine you fronted DB writes with Kafka. Lag between writing to Kafka and commit into the DB may only be 100ms, but that's "eventual". However, if you provided back a "FYI, your write is offset 1234 on partition 5", you could use that as a part of a read pipeline that checked that the DB writer was beyond offset 1234 on partition 5 before allowing the read to proceed. That'd be consistent.