Tasks are able to be automatically added to tickets upon ticket creation if the Ticket Type has a template selected as default. It should be noted that only during creation will selecting a Ticket Type cause the template to be applied. If you have already created a ticket of a different type, then edit it to select the type with a default template, that template will not be added automatically.
I tested this on my computer by going to Admin>Ticketing Applications>[selected ticketing app]>Types and selected the Type that I wanted a default task template applied to. Once I had chosen a default task template and saved the Type, I went to create a new ticket. I did this both via a Client Portal service, and via TDNext. In both cases, when I created a ticket with the corresponding type, the task template was applied upon creation.
Can you confirm how you set your Ticket Type setting for Default Task Template, and the steps you took to create your new ticket?