It’s not a phrase I convey to students so others who do might be able to respond more directly.
Instruction to students should vary. When teachers imparting ANY subject allow the sloth and torpor of rote instruction to infest their consciousness, students are no longer served. Therefore I would not give an instruction AND assert it is THE instruction.
Some students need to be moved more deeply while others need to back off. It is for this reason, among 100 others, that yoga teachers need proper training of some length and certain depth and that must be ongoing. While there are some very insightful teachers who have little training, generally speaking this requires a trained eye and a clarity of action.
More specifically your question asks about the first of three components in the practice of yoga - exploration. And it should be just that. The level of depth is being explored with the consciousness when the student places it appropriately in the physical body. You ask about pushing and while that may not be my word of choice the answer would be “Absolutely. Sometimes.”. And the same answer would come if the question were about backing off.
Sitting back like a slug means the student has no progress whatsoever. Charging in like the Light Brigade means the student likely isn’t able to feel and often haste does make waste, or worse it makes injury and setback. Taking the leg in the air in Supta Padangusthasana is nice but it is only the drawing of the leg back that effects the hamstring opening.
Approaching your maximum in postures when done mindfully is completely fine and can be very beneficial, except when doing restoratives or therapeutics and there the maximum is not done, as it defeats the purpose of the practice. And, as you approach that “maximum” and the body begins to reveal its blockade(s), work with the breath to fine tune your self-exploration and see if you can let go of some of that which you are holding.