We consider time synchronization attack against multisystem scheduling in a remote state estimation scenario where a number of sensors monitor different linear dynamical processes and schedule their transmissions through a shared collision channel. We show that by randomly injecting relative time offsets on the sensors, the malicious attacker is able to make the expected estimation error covariance of the overall system diverge without any system knowledge. For the case that the attacker has full system information, we propose an efficient algorithm to calculate the optimal attack, which spoofs the least number of sensors and leads to unbounded average estimation error covariance. To mitigate the attack consequence, we further propose a countermeasure by constructing shift invariant transmission policies and characterize the lower and upper bounds for system estimation performance. Simulation examples are provided to illustrate the obtained results.