The correct procedure is to save the beauty element without caustics and the caustics element. Then add caustics on top of beauty using the linear add operation. In Photoshop it is indeed called "Linear dodge (add)".
It is best to use 32-bit EXR.
The image can't have any VFB post-processing enabled (such as highlight compression or contrast).
Exposure adjustments should be fine (it does not matter whether you use EV -1, 0, +1, or any other value).
As mentioned before, it is best to use some proper compositing software rather than PS.