The Hatha Yoga Pradipika describes kurmasana as pressing the crossed ankles against the perineum and sitting steadily. It is a compact arrangement, everything folded toward the centre, and Svatmarama gives it in a single verse without attaching a claim to it. The Gheranda Samhita includes it among its thirty two and follows it immediately with a second form, the stretched tortoise, which is a different shape carrying the same animal's name.
Kurma is the tortoise, and in Indian religious literature the tortoise is not a neutral animal. It is the second avatar of Vishnu, who takes that form to bear the mountain on his back while the ocean is churned, and it appears in cosmological accounts as a support of the world. The manuals do not invoke any of that when they name the posture, and the atlas does not assert a connection the texts do not make.
What the texts do assume is a reader who already knows the animal's defining action. A tortoise is the creature that withdraws. The posture is the body brought in and closed, ankles at the centre, limbs gathered, and the resemblance the compilers had in mind is almost certainly that rather than the shell. Both surviving manuals carry the posture, which places it in the shared stock behind the corpus rather than among the later additions.