Billed an extra month?

To my recollection, mobility bills are for both the past and future. You are billed in advance for basic use of the options in your base plan, and for additional charges (international long distance calls, for instance), even if they are zero. 
It also seems odd you received a bill on January 13 for the period you describe. I’d have thought it would arrive in advance of the use period, so I agree with Starchoice.