Short answer: They were. What makes you think they didn't carry the gladius?

Roman cavalry auxilia carried spears, as well as javelins and long swords. The reasons for this are obvious; reach matters when you're sitting high up on a horse.

Roman auxilia on foot included both light and heavy infantry. The heavy infantry was equipped with the same gladius short sword as legionaries.

Now, auxiliary infantry did carry spears in addition to their short swords. We've found plenty of spearheads, and there are tombstones depicting auxilia infantry carrying spears. However, note the plural there. It seems most of these spears were used for throwing, just like legionary pila. Images show soldiers (probably auxilia) throwing their spears, or carrying one spear in the right hand and several more behind their shield in their left hand. That doesn't mean all spears were used as javelins, but many must have been.

The literary sources are annoyingly vague on what the auxilia did, being more interested in proper Roman legionaries. The terminology they use for weapons is, furthermore, far less precise than we would like it to be. They use the terms hasta, lancea, verutum and spiculum to indicate spears, but context shows that in most cases these could be thrown, though they might also have been used to fight hand-to-hand.

All this makes it difficult to give the reasons why some Roman soldiers carried one weapon, and others something else. Still, there are reasons why a soldier might want to use a thrusting spear in addition to his short sword. Various sources (Arrian's array against the Alans, Caesar's deployment at Pharsalus) tell of Roman soldiers being told to use spears (or indeed their pila) against cavalry, where the greater reach helped when trying to attack the rider. Perhaps more tellingly, Goldsworthy mentions an instance where the Roman first line of hastati (this occurred earlier, during the middle republic) were given the long hasta spears of the triarii to help them resist a ferocious Gallic (infantry) charge.

Sources:

• Goldsworthy, Adrian Keith. 2011. The complete Roman army.

• Bishop, M. C., and J. C. Coulston. 2006. Roman Military Equipment : From the Punic Wars to the Fall of Rome.

The responses by /u/BlueStraggler in this thread seem to suggest that the predominance of the spear over the sword in Roman Auxiliaries was due to the ease of production, simplicity of use and a smaller amount of resources needed to produce them. https://www.reddit.com/r/AskHistorians/comments/2kcyiw/what_was_the_last_battle_in_which_swords_were/