Stored value of "NOW" differs between replicas

I have a field in schema.xml defined like this:

<field name="timestamp" type="date" indexed="true" stored="true" default="NOW" />

When I perform a query that's load-balanced across the servers in my cloud, the value stored in that field differs slightly between each replica for the same returned document.

I haven't seen this field differ by more than a tenth of a second and I'm not running queries against it, but I can picture a situation where somebody has one replica returning 23:59:59.990 and another returning 00:00:00.010 and a query starts behaving oddly.

It seems like the leader should evaluate what "NOW" means and the replicas should copy that value.