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Hi, you can assign different templates to different menu links. So probably, the change of template is based on menu link change.
When you disable SEF (for test) you can see ItemId parameter in URLs and this Itemid means a menu id. You can then see if this ID changes and if yes, then try to check if such menu link is assigned to this template.
Phoca Cart, or payment methods, etc. do not have any feature to change tempalate, this is Joomla feature based on menu link.