[Q] Can do factory reset ... but it is not a factory reset

I am trying to restore the original state with 4.1.1 firmware. Downloaded I9300XXDLJ4_I9300OXADLJ4_I9300XXDLID_BTU.zip, unpacked, the installation goes without problems (Odin 3.07, Auto Reboot + F.Reset Time). And then... I am getting the unrooted phone with the same settings and apps I had before. How is that possible? Some of those apps need update (looks like some old version is "recovered"). I suspect that might have happened because some while ago I used Titanium Backup to create update.zip and "flashed" that update.zip using bootloader. But how can I make the phone "forget" about that? How can I get the "clean" factory-state phone, without those apps/settings? And, what is also annoying, straight after Odin3, the Device State is Modified (without even rooting it!). What can I do about it?

Any ideas are welcome. Thank you!