Are there any conditions that must be satisfied for assignment rules to work?

Yes, certain conditions must be satisfied for assignment rules to work,

Primarily, the module in which you create a record must have an assignment rule configured. 

Next, you need to set up conditions for particular modules — the CRM checks for these conditions during the automated assignment process.
Have a look at them:

• A lead record is assigned to a group.
• A contact record is assigned to a group.
• An opportunity record is assigned to a group AND 'Sales Stage' is not Closed Won or Closed Lost.
• A task record is assigned to a group.
• A case is assigned to a group AND 'Assigned To' is empty AND 'Status' is not Closed.
• An internal ticket record is assigned to a group AND 'Assigned To' is empty AND 'Status' is not Closed.

To know more about Assignment Rules, click here.