The process to calculate the R-squared I know is the following:

Once the terms of the regression are obtained, an ANOVA is used to assess its significance and the not significant terms are excluded from the regression equation, at this moment a determination coefficient is calculated. Then the ANOVA is run again, obtaining a different R-squared value which should be the adjusted R-squared due to the fact that now the regression equation only considers significant values.

So, does the determination coefficients for each respondent in the SSI report corresponds to the adjusted R-squared values?

In the CBC, the same doubt is for the RLH which can be seen as a similar to the determination coefficient.