Each object is essentially an Actor in the Actor Model sense. It can send messages (fetches, and responses to fetches) to other objects and regular workers. Incoming requests are not blocked while waiting for previous events to complete.
Hence, a block is only atomic if it contains no "await" statements.
In the counter example, the only thing we "await" (after initialization) is the storage put()s. Technically, then, you could imagine that the put()s could be carried out in the wrong order. But, we're able to guarantee that even though put() is an async method, the actual writes will happen in the order in which put()s were called.
(For those with a background in capability-based security: Our system is based on Cap'n Proto RPC which implements something called E-order, which makes a lot of this possible.)
* Disclaimer: At this very moment, there are some known bugs where put()s could theoretically happen out-of-order, but we'll be fixing that during the beta.