The DAX cache will not be updated. Global tables will replicate the data in other regions. However, it wouldn't update the cache. Even, the query cache
and item cache
are independent.
DAX does not refresh result sets in the query cache with the most
current data from DynamoDB. Each result set in the query cache is
current as of the time that the Query or Scan operation was performed.
Thus, Charlie's Query results do not reflect his PutItem operation.
This will be the case until DAX evicts the result set from the query
cache.
Write through policy:-
The DAX item cache implements a write-through policy (see How DAX
Processes Writes). When you write an item, DAX ensures that the cached
item is synchronized with the item as it exists in DynamoDB. This is
helpful for applications that need to re-read an item immediately
after writing it. However, if other applications write directly to a
DynamoDB table, the item in the DAX item cache will no longer be in
sync with DynamoDB.
DAX Consistency
In the above statement, you can consider the other application
word as global table
replication. The DAX wouldn't aware about the replication done for the global table.