wow... that's some pretty nice looking work for not knowing the program well... I use it daily for 10 years... but just for the same few scratch the surface things... and I have almost never use a stroke of any kind in PS, except I remember seeing it in layer styles...
but I just went to see if they have a stroke pallet like illustrator that has little corner option icons...but instead, I made a selection, went to edit>fill to get a fill... and i noticed right under that in the edit pull-down menu was stroke... so i tried that & chose "center" (which is what I see in yours too) and mine was rounded too.. then I clicked undo, & went back and assigned the stroke to occur inside my selection & got square corners.