Re: In which folder do I unzip?
Yeap, that was it. So to make it easier for the rest with same question: Follow these steps.
(a) upload new tiki version on your server.
(b) unzip it in a folder that is parallel to your existing tiki installation folder. Mine was public_html/wiki, so unzip at public_html/new_tiki (names given as examples).
(c) rename your existing wiki folder to /wiki_old. From that moment your wiki will not open (of course). This folder is your backup now.
(d) rename new version tiki folder with the name your existing installation was using (so in my case, /wiki)
(e) from here on follow the instructions found elsewhere (look for example what ricks99 writes above), in order to connect new version with existing database, upgrading your installation.
(g) enjoy