That delay is part of the new Statistics Processing Framework:
https://pkp.sfu.ca/wiki/index.php?title=PKP_Statistics_Framework#Processing_Log_Files
Currently, logging is accumulated over the course of the day, and then processing of the prior day’s log happens sometime the following day. It depends on your cron setup, or on Acron’s timing.
It should be possible to setup cron to handle more realtime statistics processing. Reprocessing a log with the same name will overrwrite the log entries that had been previously processed under that name. So, you could periodically copy the in-progress log from usageStats/usageEventLogs in your files_dir to usageStats/stage and then immediately execute the php tools/runScheduledTasks.php plugins/generic/usageStats/scheduledTasks.xml process. Just don’t move the log manually unless you know what you are doing.