Its only a stab in the dark but what about this. Your standard colour for an alert light is Red i.e. Handbreak is on. The standard colour for a warning is Amber i.e. your about to run out of fuel. So if something positive is happening i.e. your indicators are on then they use green to say, "hey this is happening, but its nothing to worry about". If they were amber as on the outside it might confuse people.
I suspect it's more a case of visibility - desireable outside the car - large and orage flashing, but less so in an occasionally dark interior - subdued soothing green to make you aware, but nothing bright enough to dazzle you.
the people outside need to be warned you are turning. or in mrsincis case that you have turned. the people inside aleady know you are indicating, but just need to be told they are working. Its an urgency difference.