From the docs datetime.weekday returns a value of 0-6
In the browser the week seems to starts on a Sunday i.e. 0 = Sunday, 1 = Monday, 2 = Tuesday, etc.
On device (and in the simulator) the week seems to start on a Monday i.e. 0 = Monday, 1 = Tuesday, 2 = Wednesday, etc.
I suggest the device behaviour is maintained and the browser behaviour corrected to match.
the browser emulator is pretty different. the biggest being that it runs way faster, but also it uses data types much larger than the system, it does not have the variable limits or the embedded item limits. it also will let you do things like have negative numbers in random functions. hopefully, they will update that thing, but I don't know if they will as it's been a while 
thanks for mentioning this one though, I've never used the day of the week thing, but I'll add it to my list of things to look out for