I am working in a State Plane/NAD83 projection. I am adding a WMTS service that is is WGS 1984 on someone else's set. When the transformation window came up, I chose WGS 1984 to NAS 1983 V. But now I am realizing that I should have said none and let it project on the fly. So I close ArcMap, remove the connection file from the ArcCatalog (C:\Users\lperdue\AppData\Roaming\ESRI\Desktop10.2\ArcCatalog) folder. Then I copy the original connection file back to the clients set. When I add the WMTS service to the mxd again and specify NONE on the transformation, the features are still offset to the north and slightly east. On my set, they lay right when they're supposed to. I tried adding the WMTS service to a different mxd on the client's set and it was still offset. I don't see anything in the Data Frame or Layer properties that indicates which transformation it is using.
I'm not 100% sure that I understand your question, but I'll describe how a few things work.
When you open the Transformations dialog, and select a particular input GCS, the transformation pull-down should list the current transformation or say "None" if nothing is set. I know at an early release, if you set a transformation, then tried to set it back to "None" that didn't work, but I don't remember for sure in which version that got fixed.
Transformations, once chosen, are put into a list of "active" transformations and that list is saved in an mxd. However, if you start over with a new mxd, you should be back to an empty list.