The Apache domain access logs are not rotated at midnight every night. Instead, they are updated every 24 hours. You can change the statistics processing schedule so that certain hours are blacked out if you prefer cpanellogd to run at select times:
"WHM Home » Server Configuration » Statistics Software Configuration"
Note that statistics applications such as Awstats or Webalizer will automatically parse the logs correctly into the correct dates/times so there is no need to have them run at midnight. In addition, statistics for each domain name are processed individually. Thus, you are not going to have them updated exactly at a certain time.