Not my area of expertise but..
The client you are using (Safari on an iPhone) should not be relevant - if it was actually connecting to the moodle site and you logging in it would be logged. It sounds much more likely that your own internet connection itself was down for some reason. That would be why your attempt to log on is not showing on the site's logs - as it did not actually go through - while the page you saw could possibly have been from your device's own cache, therefore giving you the broken link when you tried to access the quiz itself, a page you had not previously accessed.
The timings you give are confusing though - if correct: 11.30 first attempt, 15 minutes later would be 11:45 not the 12:15 reported as the server time, so either your timings are inaccurate or the server clock is out - which would be unlikely but would be easy for the technical team to check and confirm, or whether any of your colleagues had issues over the timing of the quiz closing.
To be honest, this really sounds like something you need to be evidencing with your tutor, in terms of times trying to access, error messages received, screenshots (your browser history possibly?) etc.