Then it wasn't after the events of Chrono Cross, the 10 years that passed from the moment Serge died were never actually shown.
Yes, that moment wasn't shown since the narrative is centered on Serge's point of view, who lives in a post-dimension split world. Basically, if the day when the original Kid traveled to the past was December 16, 1020 (it's just an example), then the day in which Serge talks to the Lucca ghost would be something like December 2, 1020 (just an example, accounting for the "further in the future" indication). Of course, the time travel was an event of the previous timeline, not the timeline seen in the game. On December 16, 1020 of the post-ending timeline, the event doesn't have to take place since it's already done.