Rainbow Facade Layer and Mask...

Go to the Black Shape Layer. Load the "Full Size Mask" Add a new layer. Rename the new layer to Rainbow Facade. Select > Modify > Contract... to value 3. Select > Feather... to value 2.

Rainbow Facade layer has a Mask (Selection) smaller then the Black Shape as shown in the above sample.

Spectrum Fill... into Rainbow Facade.

Select the Gradient Tool from the Toolbox. Select the Spectrum Gradient from the Tools Palette drop down Gradient List. Apply Spectrum to the Rainbow Facade Selection using the A to B spread.

Getting close but my sample includes a few more steps and they are as follows:

Place the previously created Colorized layer below the new Rainbow Facade Layer. Create a new black layer below the Colorized layer. Create a new layer under the colorized layer. Rename it Full Screen Black. Select the entire layer by pressing the Ctrl + "A" keys together. Fill the Selection with black from the Menu. Edit > Fill > and choose black from the list.

Congratulations, you are ready to work on the final Logo Text phase. If your test does not look like the sample, please read the following paragraph. Otherwise click Next.