It would be nice to inform the users of the Secondary Log shipping Database to expect a latency of around 1 hours (even though you have setup 30 mins of backup and restore interval) .
I had same case like yours and while testing how well the data are sync between the two databases, I found that there was a latency of 1 hour.
This might be because the Backup, Copy and Restore were all scheduled to run at same time (interval of 30mins). When the Restore needs the trn file to restore it to the Secondary database , It won't find it in the Restore Folder because it is in the process of being Backed-up and Copied across the network. So The Restore has to wait for another 30 mins to Restore that trn file.
Hence there is a latency of around 1 hour.
I may be able to resolve this by delaying the restore by few minutes..