Hi Aisha1985,
When a record is created in the Unified Client application we submit two requests, one to save the record and another to create an instance of the BPF process entity/table associated with the default BPF that persists the state of the BPF for the current record. When a record is not created using Unified Client application such as through automatic mechanisms, there is no instance of the BPF process entity/table for that record and as a result when the record is opened in the Unified Client application, since there is no BPF instance, the user needs to use Process->Switch Process and select the process.
So when the customer auto creates a case record, they will also need to create the instance of the correct BPF process entity/table with the required fields and then when the case is opened in the Unified Client application, the correct flow will be automatically displayed to the user.
My test:
1. I create a BPF named TMS Ticketing System as yours, and click the rule's MS flow.

2. Add a new action to create a record to TMS Ticketing System entity and set it like this:

Code view:

Note:
process id you could get it from the BPF designer URL:

processstageid and traversedpath you need send request from Web API like [Organization URL]/api/data/v9.1/processstages?$filter=_processid_value%20eq%20[process id] and then find it here:

Result:
