Welcome to the forums. A couple of comments before addressing your question:
Avoid using all caps.
Remember that you are in an international forum, so clearly explain which standards or specifications to which you are referring: For instance, you reference "Spec 346-9.1". That generally means nothing to anyone outside the state of Florida, so you are missing an opportunity to get appropriate help if your questions are vague or unclear. As an example, the American Concrete Institute has a specification number 346 that refers to concrete pipe.
Avoid using vernacular that might only be used in your area or within the context of your issue. In this case QC and VT refer to Quality Control and Verification Testing respectively, but those are not necessarily used in the same context everywhere.
Now to your question:
ASTM C31 does not state what you said. It does not require that cylinders be placed in water. It only requires that the surface of the cylinder be wet on all sides and that the environment has essentially a 100 percent relative humidity. That can be accomplished with a proper moist room or water-filled curing tanks.
The quote "At this same time" in the Florida Department of Transportation, Standard Specification for Road and Bridge Construction, Section 346-9.1 refers to the FDOT taking its verification samples (as you've termed "VT") to its lab simultaneously with the contractor's quality control (your term QC) samples being taken to its testing laboratory. The intent is that both sets of samples will be transported to their respective laboratories at the same time, so that there is little or no variation in the amount of initial field curing between the QC and VT samples.
The samples are to be done in accordance with ASTM C31 for both cases, with simultaneous transport to the labs.