API 650 5.7.8.1.e reads like this:
"The thickness, ta, of the bottom-transition plate in the assembly shall be 13 mm (1/2 in.) minimum or, when specified, the same as the thickness of the tank annular plate."
API generally intends that their statements are read as much as possibly literally, without "reading between the lines" or trying to figure out what they really meant or adding words that are not there. Statements with more than one clause should not be taken apart, the entire sentence should be read as one.
If they meant the greater of 1/2" and the annular plate thickness, they would have said that. If they meant the lesser of 1/2" and the annular plate thickness, they would have said that. If they meant "nominal thickness" or "corroded thickness" or "thickness exclusive of corrosion allowance" they would have said so. It is not up to us to try and figure out why the section was written as it was, but to follow it as much as possible exactly as it is written. If we think there is an error or a confusing statement, we submit an inquiry.
You could substitute colors for the selections, perhaps that would clarify it. The sentence then reads: "The thickness, ta, of the bottom-transition plate in the assembly shall be BLUE or RED. BLUE is 1/2" minimum and RED is when specified, the same as the thickness of the tank annular plate. Why did they allow you to increase BLUE beyond 1/2" by using the word "minimum" ? We don't know.
The section reads 1/2" or the annular plate thickness if an annular plate is specified. I read this exactly as it is written: if an annular plate is specified, use that thickness, if not, use 1/2". Pretty clean and clear. They used the word "or" and I take it to mean "or", not "the greater of" etc. Corrosion allowance is not mentioned so it is not intended to be applied. Note that corrosion allowance is a factor when determining the annular plate thickness so if an annular plate is specified and the transition plate is the same thickness, it has the same corrosion allowance. If an annular plate is not specified, then the minimum thickness is 1/2". You can make it thicker but not thinner.
On the other hand, the client is the final arbitrator on issues and questions, you may have to do as they ask.