Hi Avik
First as a side note to the readers, we do not recommend to use Display conditions for page security on most objects, as this is affecting the performance of the application, having to always run the condition before displaying the results. What we recommend is using Secure Subpages instead.
However there are exceptions on some objects as we do not have security at Task level, so Avik you were very correct to look there. Unfortunately you seem to be hitting a known issue:
CLRT-72692 Value always displays on Clarity Gantt regardless if Subpage Display Conditions are met
http://www.ca.com/us/services-support/ca-support/ca-support-online/knowledge-base-articles.tec1824111.html
Because this was not planned for fixing in the product, the only possible suggestion I see here is to work on the Permissions the users have, more specifically, the following rights:
Project - Edit Assigned Tasks
Project - Edit Management
in conjunction with setting up Audit on the affected attributes - determine which users are doing the incorrect changes and revoke their rights when appropriate. See if that can help avoid the issue.
I hope this helps -Nika