It's all about energy management - and I'd prefer that when I get that sinking feeling I'd instinctively respond with throttle rather than stick - apart from that, both methods produce the same outcome and neither is right or wrong. And in the real world, on approach for instance, we make frequent small simultaneous changes to both, we would hardly notice which came first anyway, it pretty much becomes instinctive.
Nevertheless - in terms of aerodynamics, the natural aerodynamic behaviour is that stick controls speed (more correctly, AoA - but in most GA aircraft speed is a good proxy for AoA) - after all that is what decalage is all about. As others have pointed out, that normal aerodynamic effect is modified in some aircraft by effects such as the thrust/drag couple.
And, as Destiny pointed put, pulling back on throttle actually increased airspeed first, then returned close to trimmed speed - but the aircraft started to descend rapidly. As predicted. Then increasing throttle without touching anything else resulted in a climb at marginally below trimmed speed.
And as Mazda rightly points out - don't get your advice off a web site. Always talk to your instructor and take their advice. :thumb_up: