There are three options to trigger Rules and apply Actions using Automation 'On Creation', 'On Edit' and 'On all Tasks Completed'.


Fig 1 - Trigger Options


The 'On Edit' trigger will apply your rule when you edit specific existing records.  Such as Editing existing Contract details, or adjusting Contract Financial information or changing a Linked Contract Person to another. 

So your Rule could be:


'On edit' of a <Contract>, create a <Task> for the <Contract Manager>.


If you do not add any Criteria to your Rule then it will apply to all of your Entity records, if you wish the Rules to apply in certain circumstances then you must specify when the rule should apply using the Criteria.