Almost, the Pre-Marian Reform Formation was set up into 3 basic lines, the Hastati at the front, the Principes after them, and finally the Triarii (Each line had consequentally more experienced troops, with the Triarii being the most experienced in the legion), this is where the term "ad triarios rediisse" ("Falling on the Triarii) came from, as the Roman commander would have to be desperate to send them into battle, there was also a group of Velites during the 2nd Century BC (Mostly), that was composed of the earlier Rorarii and Accensi, and we're used as skirmishers before the battle begun (Much like your tactic for drawing the enemy to the center, they would throw javelins and then retreat)
I usually try to engage in a line and then use my Cavalry to crush demoralized units (This is my "regular" tactic, I use others when the conditions doesn't allow it)
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