Patch compliance reports don't include the execution start and end time on computers.
The attached 'Patch Policy Execution in the last N Days by Computer' report will show this information along with more details.
ITMS 8.x
Patch Management 8.x
Download the attached .xml file
Go to NS Console> Reports> All Reports >> Right click on <Your desired folder> and choose 'Import', and import the .xml file.
This report shows the File and Policy name with the start and end-time of the execution along with the current status of the update.