Here's some more data. I'm running v2.2 with Europe/London set for timezone and Day, Month, Year set for field order in general Admin.
I've now added all four of the calendar module variants to test them with either the 1st day set as Sat, Sun or Mon. The modules, shown from top to bottom, are:
The attached screen shots show that when Sunday or Monday is set for the 1st day the two 'new' (pretty) format modules correctly show either Sunday or Monday as the 1st day but both are 'out' by one day for the date ie Friday 13th Feb is incorrectly shown as Fri 12th Feb. When Sat is set as the 1st day these two 'pretty' modules do NOT show Sat as 1st day - it stays as Mon and the date is now 2 days 'out'.
Interestingly both 'old' style modules always show Sunday as the 1st day and always show the correct date.
I think this must be a bug of some sort.