Airbus and most probably also Boeing don't give a value for tail wind for its CFM fitted aircraft.
The reason is simply that it depends not only on the wind, but also on other parameters, I can imagine the state of the engine, the temperatures aso.
So AI recommends to do a manual start whenever you have tailwind, knowing that most of the time people wont do it
But they are covered if something happens. CFM and IAE engines have proven to be very stable even with strong tailwind conditions during startup.
hth,
Dani