Basically when you initiate the snapmiror relationship until the the complete data copy is transfered , snapmirror status will be in "uninitialized and transfering status " which means currently data copy is in progress. Once the data is copied you will see as "Snapmirrored and Idle" status which means data copy completed and are in sync.
The only thing you want to make sure is using snapmirror status -l <destination full path" and check out whether the data is moving or not , under the KB transfered you will see the number of data is moved etc..that is the confirmation of data copy is in progress. Use the command to know the exact status of the copy,
snapmirror show -destination-path filername:<dest_vol> -fields status,last-transfer-size
Expected outcome current :
source-path destination-path status last-transfer-size
<source path> <destination path> Transfering <in MB's >
If the last transfer size is increasing then the copy is going good. Finally you will see as "Snapmirrored Idle"
Thanks,
Kannan