Sharepoint - SharePoint Online Search Crawling

As far as I know in the Office 365 / SharePoint Online, you don't have any control over the schedule for the crawl. This is managed by Microsoft.

SharePoint Online targets between 15 minutes and an hour for the time between upload and availability in search results (also known as index freshness). In cases of heavy environment use, this time can increase to six hours. http://www.sharepointnutsandbolts.com/2013/10/waiting-for-search-crawl-in-office-365.html

You can request a particular list or library to reindex. This can be done in the List Settings ==> Advance Settings click Reindex Document Library

Continuous crawls help keep search results fresh by frequently crawling content in SharePoint sites. Continuous crawls are enabled in SharePoint Online, with crawl frequencies managed by Microsoft. In SharePoint Server 2013, administrators can enable continuous crawls and manage continuous crawl frequencies. Learn more about default crawled file name extensions and parsed file types in SharePoint. Learn more aboutmanaging continuous crawls.

Reference : https://technet.microsoft.com/en-in/library/sharepoint-online-search-service-description.aspx