Do I need a jack "puck" or jack adapter with the Modern Spare jack when raising my Tesla?

No, the Modern Spare Jack for your Tesla Models is designed to be used without additional adapters.

The jack included in your complete Tesla spare tire kit is specifically designed to be used without an additional “puck” or jack adapter. The existing jack head is designed to function properly at your Tesla's lift point. 

Please note-

It is extremely important that you identify the exact lift point locations for your Tesla. Raising the car by not using the designated lift points can result in severe damage to the car and possibly to the main drive battery assembly.