I think I can help you here! Here's the applicable text from Livy (sorry...it's very long!)  

After making trial of their strength in these slight engagements, Hasdrubal led his forces to the field; then the Romans marched out. Both armies stood in order of battle under their respective ramparts, neither party choosing to begin the attack; when it was near sunset, the Carthaginians first, and then the Romans, marched back into camp. They acted in the same manner for several days, the Carthaginian always drawing out his troops first, and first giving the signal of retreat, when they were fatigued with standing. Neither side advanced in the least, nor was a weapon discharged, nor a word uttered. The centre divisions of their lines were composed, on one side, of Romans; on the other, of Carthaginians and African auxiliaries: the wings were formed by the allies, who on both sides were Spaniards. In front of the Carthaginian line, the elephants at a distance appeared like castles. It was now generally said in both camps, that they were to engage in the same order in which they had stood before; and that their centres, consisting of Romans and Carthaginians, who were principals in the war, would no doubt encounter each other with equal courage and strength of arms. When Scipio understood that this opinion was firmly entertained, he took care to alter the whole plan against the day on which he intended to fight. On the preceding evening, therefore, he gave out orders through the camp, that the men and horses should be refreshed and accoutred before day; and that the horsemen, ready armed, should keep their horses bridled and saddled. Before it was clear day, he despatched all the cavalry and light infantry, with orders to charge the Carthaginian outposts; and immediately advanced himself with the heavy body of the legions, having, contrary to the expectation both of his own men and [25] the enemy, strengthened the wings with his Roman troops, and drawn the allies into the centre. Hasdrubal was alarmed by the shout of the cavalry, and, springing out from his tent, saw a bustle before the rampart, his men in hurry and confusion, the glittering standards of the legions at a distance, and the plain filled with troops. He immediately despatched all his cavalry against that of the enemy, marching himself from out the camp with the body of infantry; but, in drawing up his line, he made no alteration in the original disposition. The contest between the horse had continued a long time doubtful, nor could they decide it by their own efforts, because, when either were repulsed, which happened to both in turn, they found a safe refuge among the infantry. But, when the armies had approached within five hundred paces of each other, Scipio, giving the signal for retreat, and opening his files, received all the cavalry and light troops through them; and, forming them in two divisions, placed them in reserve behind the wings. When he saw that it was time to begin the engagement, he ordered the Spaniards, who composed the centre, to advance with a slow pace, and sent directions from the right wing, where he commanded in person, to Silanus and Marcius, to extend their wing on the left, in the same manner as they should see him stretching on the right, and attack the enemy with the light-armed forces of horse and foot before the centres could close. The wings extending in this manner, three cohorts of foot, and three troops of horse from each, together with the light infantry, advanced briskly against the enemy, while the rest followed them in an oblique direction. There was a bending in the centre, because the battalions of Spaniards advanced slower than the wings, and the wings had already encountered, while the principal strength of the enemy’s line, the Carthaginian veterans and Africans, were still at such a distance, that they could not throw their javelins with effect, nor did they dare [26] to make detachments to the wings, to support those who were engaged, for fear of opening the centre to the forces advancing against it. The Carthaginian wings were hard pressed, being attacked on all sides; for the horse and foot, together with the light infantry, wheeling round, fell in upon their flanks, while the cohorts pressed on them in front, in order to separate the wings from the rest of the line. The battle was now very unequal in all parts; not only because an irregular multitude of Balearians and undisciplined Spanish recruits were opposed to the Roman and Latine troops, but, as the day advanced, Hasdrubal’s troops began to grow faint, having been surprised by the alarm in the morning, and obliged to hasten out to the field before they could take food to support their strength. With a view to this, Scipio had taken care to create delay, for it was not until the seventh hour that the battalions of foot fell upon the wings, and the battle reached the centre somewhat later; so that, before the enemy began regularly to engage, they were enfeebled by the heat of the meridian sun, the labour of standing under arms, and by hunger and thirst, distressing them at once. They stood, therefore, leaning on their shields; for, in addition to their other misfortunes, the elephants, terrified at the desultory manner of fighting used by the horse and the light infantry, had thrown themselves from the wings upon the centre. Harassed thus greatly, both in body and mind, they began to give way, but still preserved their ranks, as if the whole army were retreating by order of the general. The victors, perceiving the superiority which they had gained, redoubled the fury of their assault on all sides, so that the shock could hardly be sustained. Hasdrubal, however, endeavoured to stop his men, crying out that “the hills in the rear would afford a safe refuge, if they would but retreat without hurry;” yet fear overcame their shame, and although such as were nearest the enemy still continued to fight, they [27] quickly turned their backs, and all betook themselves to a hasty flight."  

So lets break this down...The days before the battle, the Romans and Carthaginians lined up in the order of battle, but no battle took place. They each lined up the same way each time (Romans/Carthaginians in the middle, Spanish allies on the wings), stood there till it was dark, and went back to camp. This was Scipio's plan the whole time (which would not have worked if the Carthaginians would have attacked first). After he believed that Hasdrubal was set on this way of assembly, he changed the plan with orders to attack the next day. He switched his battle plan to have the Spanish allies in the middle, and the Romans/Latins on the wings. Starting the battle with an early morning cavalry attack, he surprised the enemy, preventing them from eating breakfast, but most importantly, not giving them time to re-arrange their battle formation to match the new Roman formation. The Roman (Legion) wings were instructed to extend and attack the enemy (Spanish) wings, while the Roman center (Spanish allies) was instructed to march slowly against the enemy (African) center. This was the crucial part of the whole battle. It's not that the Roman Spanish allies were expected to be the weak link and be pushed back, it's that the enemy wings were expected to be the weak link and get pushed back by the Roman legions...the center was the last part of the Roman attack to meet! The elite African center of the Carthaginians could not turn to help the wings due to the impending attack by the Roman center (while the center was marching slowly, they most certainly would have rushed into the attack had the Carthaginian center turned to help the wings). Scipio coupled this with delaying the attack as long as possible to take advantage of the Carthaginians not eating. Combined with the elephants running over their own men, the battle ended with a complete Roman victory. I hope I was able to clear this up for you...sorry for the long post!  

tl;dr: The Roman wings attacked Carthaginian Spanish wings first, the Roman Spanish center attacked Carthaginian African center last. It was a pincer attack due to the legions beating the weak Spanish, not the other way around.