Support Team replied the topic: Cache page and autotweet cron with joomla 3.7
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System - Page Cache plugin is an optional cache technique that takes advantage of the browser case.
It is not a default option in Joomla, because it is not recommended for general dynamic sites.
Joomla 3.7 could bring additional improvements that force a browser cache to the web cron job task. It's a known issue, that the browser cache frequently prevents the execution of the web cron job task.
For these cases, you can schedule the execution of the cron job task with a command line. In this way, you totally avoid the execution through the web server: