AvatarNathan Richer

first, i am not a clinician or a researcher so i could not tell you exactly what is happening or supposed to happen. that is why this is a cue and not a description of what exactly happens.

suffice to say that you need to have a lot of tension in the bracing, rising as the load does. that is why the cue is to pull yourself down into position with hams to calves and abs to top of quads. i believe this activates more fully all muscles required, as we are a quad dominant society and if we don’t pull down into position (versus letting gravity drop us into position), we will inevitably over-engage our quads, which leads to knee pain, etc.
definitely don’t let the glutes relax – if you do then the legs might lose their stability in ext rotating and start drifting inward. i’m just commenting on the fact that tensing glutes usually results in a concentric contraction which wants to keep you up. 
if you ext rotate at hips, you will have to engage the glutes as the glutes help drive the femurs out and it stabilizes the whole thing. so i think a better cue than thinking about individual muscles like flex glutes, is to ext rotate the femurs out which will not only engage glutes but also all other leg ext rotators. as kstarr says, this creates the super stable position at the hips, and then your body knows what to do from there. if you lose tension (ie. ext rotation), all sorts of things will go wrong like lumbar spine rounding and butt winking.
so i’ll add this – organize yourself with 20% bracing in torso and glutes, and before you descend torque your femurs outward into ext rotation. then descend.
also you don’t want to tuck your pelvis at the end or else that leads to butt winking. if you have created enough space between the legs at the hips and have sufficient mobility your pelvis should be in the correct position. 
but yes squeezing glutes will help engage the high hams and keep your pelvis neutral and not letting it hang out in anterior tilt. and if you can engage the high hams by themselves, do that too!