This is really informative.

Yes, I want to analyze their data and run fwhmx + 3dclustsim (this method seem to be a bit less conservative compared to 3dttest++ -clustsim or -etac) and see if we ge the same results.

I suspect that using pars of 1-sided t-test have been used.

Is that when e.g. you have two conditions (e.g. iaps images and shapes) and two groups (controls and patients) and you would run:
1 ttest iaps vs shapes for controls
1 ttest iaps vs shapes for patients
follwoed by a ttest vs the coef comming from these two t-test and thus missing the variance between the groups? Or what do you refer to?

Also, how would you adjust the p-values?

Thanks! I will get back to you if we run this test!