In an atemporal relational database, there is a convention that the predicates don't explicitly mention time, but rather refer implicitly to a single world situation at a single moment in time.
To the extent that the relvars correctly record the extensions of their predicates about the world, they should be synchronised with the world as it changes. But of course, there are delays (inevitably because information cannot propagate faster than the speed of light), and of course manual data entry by users involves delays.
In other words, the reality is normally that the information going into a database comes from asynchronous sources, and the idea that the database records a synchronous snapshot of the world is a fiction.
It doesn't seem possible to make the predicates explicitly account for lags in the updates to the relvars.
Nevertheless, at least for a database on a single machine, it is usual for transactions to allow changes to multiple relvars to be made atomically, and therefore it's usual for constraints to be imposed across relvars on the assumption that they are updated synchronously.
But it's not a good idea to try to synchronise updates to multiple databases in a distributed system. Distributed transactions are an anti-pattern.
It seems necessary to treat the relvars that are not synchronised as belonging to independent logical systems (microworlds).
This eliminates the logical contradictions because it is no longer assumed that the relvars record conflicting information about the same world situation.
Presumably such contradictions tend to be short lived and are only an artifact of asynchronous updates, and the conflicts should disappear at quiescence.