There are a lot of potential complexities with your question. Let me take a stab at it.
First, please recognize that you should NOT use zero-centered diffs (normalized) utility rescaling with the Exponentiation function. One must use the raw utilities if wanting to convert utilities into probabilities of choice. The zero-centered diffs (normalized) utility rescaling is way too extreme to apply the exponentiation transformation to.
Next, if you are using our software to create linear terms for price (such as with our logit, latent class, or HB estimation), then no matter what values you type into the "value" column within the Attribute Coding dialog, the values will be zero-centered when the design matrix is created within the software and the utilities are estimated.
The documentation explains this. For example, in Lighthouse Studio, the documentation for the "Value" field says, "Please note that CBC will automatically zero-center any values you specify when creating the independent variable matrix. So, values of 1, 2, 6 will be converted to values of -3, 2, and +3 in the independent variable matrix prior to utility estimation."
Now, our market simulator recognizes its internal procedures when computing the total utility of a product concept (it knows it needs to take zero-centered price values and multiply them by the raw price coefficient); but if you are doing computations on your own, you'll want to keep this in mind.
For a CBC study that doesn't have a None concept and where all the attributes are common across all product concepts (not alt-spec design), it doesn't matter whether you remember to zero-center your price values prior to multiplying by the coefficient because a constant utility added to each product alternative factors out in the logit rule math.