By default, conversions are not tied to Piano templates in case of a simple button redirect click from within a template.
If you want to assign conversions to a specific experience and/or template, you'll need to use the params model that is available inside the template's scope.
To do this, you can add external-event-params="{{params}}" to the button inside the Piano template.
Now, when using the checkoutCustomEvent callback, you'll have the params object available in the response, which contains the tracking parameter trackingId.
As the last step, you would now add the query parameter '_ptid=' + trackingId to the URL linked within the button available within the params model.
Now, with the trackingId in the URL, you'll be able to track conversions from this template's button.
Please note, that this approach can be used for clients who use Piano Management + Billing checkout on a separate landing page. It does not apply to clients using external checkout.