Caesar was born, best estimate, 100bce, and Spartacus was defeated by Crassus circa 72/71 bce. Caesar was not even a dot on the horizon by this time. It is true that he may have had political connections with the Marian party, but he had no actual power. Caesar came to prominence in 62bce, a full decade after the third servile war.
Any use of Caesar's name by tv is no doubt a result of producers trying to cash in on his fame and the fact that very few non-historians have heard of Pompey or Crassus.
I often lament tv's tampering with history, it is actually more interesting than their Hollywood view of the world.
See Plutarch's life of Crassus for history's only significant mention of Spartacus. Check also the life of Pompey for how he stole the victory of Crassus, and the life of Caesar for no mention of the event at all.