I've just done an upgrade from a very early v6.1.x to latest 6.2.8 and I found I had this error, I changed the following to cure it:- Store settings > Advance > Time zone and changed the timezone from London/Europe to disabled and the errors stopped. fortunately my server is on the correct time. I wonder if the UTC offset box above will adjust it if the time is out? i have that box blank. list of off sets can be found here https://en.wikipedia.org/wiki/List_of_UTC_time_offsets
i've just googled "controller.index" and came across this thread from 2015 shame the images don't seem to be appearing in my browser on the thread to see if its the same. It might be an exploit if you didn't place the code there and don't recognise it.