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The backup happened immediately as Remote Control's schedule is "greedy". With your settings, it supposes that every 31st of every month it has to take a backup. Since no backup was made on April 30th or later, it supposes the backup is out of date and runs a backup immediately. Your next backup should be made either on May 31st or June 1st.

Regarding the log, that's expected. Remote Control does three things:
1. It takes a new backup. This is what creates the log entry and, rightfully, Akeeba Backup must not delete the backup file just yet!
2. If the previous step is successful, it downloads the backup archive. This happens outside of the backup loop and doesn't get logged on the server side (the Akeeba Backup log file you saw). It only gets logged on the client-side (the Akeeba Remote Control log file).
3. If the previous step is successful, it removes the backup file from the server. Just like the previous step, this is only logged on the client side, not the server side.

In short, only the actions performed during the backup/post-processing loop are logged on the server side. Downloads and removals of backup archives are out-of-loop operations and are only logged on the client-side which is the one initiating them.