Does the prayer of one who prostrated, then rose from prostration, then his imam prostrated so he prostrated with him again, become invalidated?

If the Imam rises from the first prostration and sits between the two prostrations, while you rise from the first prostration and the Imam performs the second prostration, your prayer is valid. You should sit between the two prostrations, then follow your Imam in the second prostration. The prayer is not invalidated by lagging behind by one pillar.