Actually, both spin and jump work for that jump, and have since 2.0. You can jump anytime you're not in your falling frames with the Whirlwind Shield. If you don't know about the feature it can definitely kill you the first few times, but after that it can be a lifesaver, especially in levels like NAGZ, where you're trying to do precision platforming and land on the platform with too much speed and fall off by just a tad. In those situations it's great for getting back on the platform and to safety if you have some quick reaction time.
The trigger when Tails is panting is a bug, though.