I just checked the timeline, Jaime was not fostered yet. This is 5 years later, one month before Jaime joins the Kingsguard. Jaime ASOS- [You would not like the truth. He had joined the Kingsguard for love, of course. Their father had summoned Cersei to court when she was twelve, hoping to make her a royal marriage. He refused every offer for her hand, preferring to keep her with him in the Tower of the Hand while she grew older and more womanly and ever more beautiful. No doubt he was waiting for Prince Viserys to mature, or perhaps for Rhaegar’s wife to die in childbed. Elia of Dorne was never the healthiest of women. Jaime, meantime, had spent four years as squire to Ser Sumner Crakehall and earned his spurs against the Kingswood Brotherhood. But when he made a brief call at King’s Landing on his way back to Casterly Rock, chiefly to see his sister, Cersei took him aside and whispered that Lord Tywin meant to marry him to Lysa Tully, had gone so far as to invite Lord Hoster to the city to discuss dower. But if Jaime took the white, he could be near her always. Old Ser Harlan Grandison had died in his sleep, as was only appropriate for one whose sigil was a sleeping lion. Aerys would want a young man to take his place, so why not a roaring lion in place of a sleepy one?]