What a ridiculous argument-the most important point here is that your instructors are not follwing a common standard-potentially much more dangerous than splitting hairs over when and where to apply carb heat.
The role of the CFI is to set the training policy based on the engine manufactures instructions and any directives published by the CAA. The role of instructors should be to follow that policy or work elsewhere. Schools that operate with instructors doing their own thing, usually based on folk lore, only serve to lower training standards.