The authorised companion book ("An Activist Survival Guide" written by Maria Wilhelm and Dirk Mathison in consultation with James Cameron) explicitly states that supra-luminal communication is commonplace in the Avatar universe, albeit extremely expensive. Data can be shared between two "entangled particles" at a rate of three bits per hour and at a cost of approximately $7500 per bit.
At best guess, even with extremely high compression rates, the message length required to communicate the need to replace Tom Sully with his identical twin would therefore have cost hundreds of thousands, if not millions of dollars.
By the same token, a message would be sent to Earth to expect the arrival of the expelled military. This message would arrive six years ahead of the ship.
As far as time dilation is concerned, the Avatar Wikia suggests that relativity is an issue for transport ships which experience a dilation ratio of around 1.6:1 (I've been unable to locate a canon citation).
Also notable are the time dilation effects experienced at higher
speeds; an Earth-time voyage of 6.75 years seems significantly shorter
at 0.7 times the speed of light. In accordance with Einstein's theory
of relativity, from the crew's point of view it is only four years'
travel due to time dilation