Only later did this tantra come to be interpreted through creative commentary as being about tummo.
From what I can tell, tummo as practiced today has no textual justification save for a couplet from the Hevajra tantra.
Not that it matters, since these things were taught by omniscient Mahasiddhas.
As I mentioned, the tummo in the new tantra schools for the most part depend on Krishnacarya's instruction. However, tummo also shows up in the Sahajasiddhi of Dombhi Heruka.
It seems that indeed Tummo was adapted to Cakrasamvara from the Hevajra system, perhaps because the Samputa tantra is a common commentary to both. The Tummo instructions which are given a verse in Hevajra are elaborated in the Samputa tantra in a section called the Vasantatilaka (which is also a meter in Sanskrit poetics),"the ornament of spring" which may be found in the sixth kalpa of the Samputa (the Samputa is divided into ten kalpas, each having four sub-sections, for a total of roughly forty chapters).
The earliest completion stage manual we have on Cakrasamvara is Ghantapada's five stages (not to be confused with Nagarjuna's five stages connected with Guhyasamaja). Caṇḍalī yoga (gtum mo) is distinctly absent from that text. However, in the outer five deity sadhana written by Chogyal Phagpa, the completion stage given for that sadhana is directly based on subsection two of the sixth section of the Samputa. Perhaps it is because this tradition comes from Mardo Lotawa who also translated Krishancarya's Vasantatilaka.
The completion stage manuals of Krishnacarya all center around the concept of the Vasantatilaka, and one of them is explicitly named as such. Krishnacarya writes that vasanta, spring, means "when the wind ceases, after the breath of the right and the left goes into the nostrils". This Vasantatilaka was also translated by Mardo.
As a testament to the enduring popularity of the Vasantatilaka system, Vanaratna, the last Indian Mahasidda to visit Tibet (15th century) wrote a commentary on Krishnacarya's text some 40 folios in length which is also preserved in the Tengyur.
It is in the commentaries by Sachen on the Krishnacarya corpus that we find the clearest indication of the process of attaining rainbow about according to the Cakrasamvara system in the Sakya school.