I am using the MICOM procedure to test for measurement invariance among groups in PLS SEM modelling . This procedure consists of 3 steps, where in step 3 one tests for equality of composite means values using a permutation test: "we apply PLS to obtain construct scores, using the pooled data. We then examine whether the mean values (and variances) between the construct scores of the observations of the first group and the construct scores of the observations of the second group differ from each other. Full measurement invariance would imply that (both) differences equal zero (or are at least non-significant)." 
Using SmartPLS, the results for one of my latent variables in step 3 of the MICOM procedure are as follows:
EDIT: Changed CI 5% to CI 95% (it was a typo). See first comment and response
Orig. mean diff.: -0.264; Mean - Permutation Mean Diff.: 0.001; CI 95%: [-0.056, 0.056]; p-value: 0.000
Orig. mean diff. is calculated for the original groups, using the observed data. More specifically, for a given LV, its composite scores are calculated for all observations (i.e. using all the data, from both groups) using PLS-SEM. Then, for each group, the mean of the composite scores corresponding to observations within that group is calculated.
Orig. mean diff. is the difference of the calculated means.)
So, according to the p-value, the difference of means is statistically significant, so there is no full measurement invariance. However, in page 416 of the MICOM paper , the authors say: "If the confidence intervals of differences in mean values (and logarithms of variances) between the construct scores of the first and second group include zero, the researcher can assume that the composite mean values (and variances) are equal. In this case, full measurement invariance has been established"
In my case, the CI includes zero, so according to the paper we could claim that the composite mean values are equal. This is in contradiction to what the p-value says. So how should I interpret this result?
On a side note, how is the CI calculated here? When reading literature about permutation tests, I always read about calculating p-values, but no CIs.
 Henseler, J., Ringle, C.M. and Sarstedt, M. (forthcoming), “Testing measurement invariance of composites using partial least squares”, International Marketing Review.