Calander events shifting days
This has happened to me on my Samsung Note 4 just recently under similar circumstances. I don't cross timezone and it had nothing to do with a time change because none happened. I'm also using Lollipop 5.0.1 so it doesn't appear to be an OS issue.

Mine was in the Google Calendar, not the phone's default one also. It did seem that it shifted after I synchronized the calendars with Google. It only happened to the event I had sat as reoccurring on an 'every other' setting.
I'm guessing it may be a bug in the synchronization system trying to figure the days when having sat them with a 'every other whatever' type setting. 

I fixed this error by editing the event (selecting ALL events) then moving it back to the correct Saturday and editing the occurrence to 'every second Saturday of the month' as it was and it seemed to correct all of them when synchronized.