This is a normal behaviour in Sitecore, you need to add agents for schedule task on CD.
You need to add in your config files :
<configuration xmlns:patch="http://www.sitecore.net/xmlconfig/" xmlns:xdt="http://schemas.microsoft.com/XML-Document-Transform">
<!-- adjust the value according related infrastructure -->
<sitecore>
<scheduling>
<agent name="Web_Database_Agent" type="Sitecore.Tasks.DatabaseAgent" method="Run" interval="24:00:00">
<param desc="database">web</param>
<param desc="schedule root">/sitecore/system/tasks/schedules</param>
<LogActivity>true</LogActivity>
</agent>
</scheduling>
</sitecore>
</configuration>