Exchange Mailbox moves and transaction logs

So I have a DAG and the databases are replicated.

If I move a 5 GB mailbox from Database01 to Database2, what should I expect to find with the transaction logs?

Should I see the log files grow by 5 GB in Database02 Log directory?

I kinda expect the logs to grow for the target, but not the source. But I am also seeing my source database logs grow.

Thanks!