I don't know about NJ, but in many states, a traffic offense prosecution is a criminal proceeding, and the same burden of proof is in effect--beyond a reasonable doubt. In a real criminal case, before a jury, cell phone records would have to be certified as business records in some fashion (either by a certificate of regularity or by testimony of someone who's familiar with how records are kept)) before they could be received in evidence. However, in a traffic proceeding, the judge/hearing officer will likely just accept the records without their being certified.
Here's my guess---the supervisor who claims he saw you talking won't appear. The guy who wrote the ticket will. In a real court, in a real case, he couldn't testify that "my supervisor radioed me and told me that the driver of (insert plate # or vehicle description here) was talking on a cell phone", as that would be hearsay. In traffic court, things aren't as formal. But, the fact that the ticketing officer didn't witness the infraction himself, pout 12:06 down as the "time of offense" on the ticket, and your records showing your last call 10 minutes before, and your own version of the facts, will probably sway the judge to dismiss the ticket. Cops will always go by the time and other information on the ticket, because by the time of the hearing, they won't remember many of the finer details. The fact that you may have access to several cell accounts wouldn't be determinative, unless the burden was on you to prove your innocence beyond all possible doubt. And that's not the way it's supposed to be.
Bring the little flosser-thingamabob that you use with you to court, and demonstrate how you were holding it to the judge. If nothing else, he'll give you props for giving him a chuckle. These guys hear the most boring, hashed-out testimony from cops and lame excuses from offenders all day, day in and day out. Something new and different like this will be appreciated.