Sounds like you have Quantize On, and you have the "Start at Beginning of Track" setting checked (not sure what it is really called but it is in settings). If Quantize is on, and Rekordbox is set to automatically start at the beginning of a track, it will look to start at the first beat it sees as defined by the beat grid. If Quantize is off it will start at the actual begiining of a track (even if it is not on the grid). Also is you don't want it to start at the beginning of a track just change the setting.