I am following a protocol described in this paper by Ma et al: Removing endotoxin from plasmid samples by Triton X-114 isothermal extraction.

They state:

Triton X-114 isothermal extraction was performed as follows. After 1 volume of DNA sample was mixed with 0.2 volume of TXS solution, the clear mixture was incubated at room temperature for 10 min. After adding 5 M NaCl to a final concentration of 1.0 M and mixing well by hand shaking, the mixture was centrifuged at 12,000g in a microcentrifuge for 10 min at room temperature. The upper aqueous phase was transferred to a fresh Eppendorf tube, and the extraction procedure was repeated two more times.

Here they are using SDS and NaCl to circumvent the need for temperature shifts when removing endotoxin with Triton X-114. However, the last sentence is not clear to me. In contrast to the first extraction, for the second and third repeates there is still NaCl in the solution from the first round. Thus, adding more TXS solution results in immediate clouding. Do I just centrifuge immediately? Or do I incubate for 10 minutes even though the micelles have already formed?

I have inquired of the authors for clarification, but I wonder if any of you experts on cloud points, endotoxin, and/or solubility have any perspective?