I was looking to get TS10 for my car as well. Inquire Tirerack and got this response:
"Enkei wheel is not compatible with GR Corolla because the studs on this vehicle are too short to allow the Enkei wheels to fit. They would need to replace them with longer hub studs."

Is your car having the original studs? And can you confirm how many turn of lug nuts when install those wheels with its lug nuts?
And are lug nuts for this wheel set conical? Or are them flat like OEM lug nuts? Any possibility to post a picture of lug nuts that comes with this set of wheels?

 

-Car has the OEM studs.
-I don't remember how many turns I got, I only had the wheels on the car once and that was after the 1st autocross event in July. But in 20 yrs of swapping wheels for autocross/rallycross, nothing felt out of the ordinary. Probably drove it a month/about 1K miles until the next autocross and swapped the RE71s back on.
-I'm adding two photos of the lug nuts and wheel locks that also come with.

Tirerack can be a bit misleading. I ordered new tires for my Celica this summer, they called my cellphone to warn me the tire size wouldn't fit the wheels I had. I let them know I was already using that size & merely replacing with the same thing.