I'm a bit puzzled about the USB socket '5V'. If that's 5.0V from the PC, doesn't that imply only about 4.4V on the Tiny? Or 4.8V if it's a germanium diode?
It's probably a Schottky diode with a drop of about 0.3 ~ 0.4V, though that schematic shows a "regular" silicon diode with a 0.6 ~ 0.7V drop.
Nano's use that scheme and usually have a Vcc of 4.6 ~ 4.7V
My spec sheet for the S4 diode says:
Schottky barrier diode
40V @ 350mA continuous and 1.5 A repetitive @t<=1.0sec.
Vf = 0.37V @ If = 20mA and 0.6V @ If = 200mA.