Yes, I’d say this is “standard” implementation, given the way you’ve set it up. In this case, I think if you set up a similar arrangement in Photoshop, using layers and a layer mask (your alpha channel image), you’d get similar results, if you use a normal blending mode.
Keep in mind that “overlay” is not the same as “alpha over” – two different blending modes – plus you can never rely on an exact match between apps in how such things are accomplished. For example, Photoshop layering with a layer mask is very similar to Blender’s alpha over, and in most cases looks the same, but can sometimes look noticeably different, depending on settings, nature of the matte/mask, and other aspects.
Better to find what works to accomplish a certain end in whatever app you’re in at the time, with correlation between apps as a guide.