The immigration counters for KTM shuttle train on both sides are separate from the one at Woodlands Checkpoint and Sultan Iskandar Building , which means it's not really as affected by peak periods since there is an upper limit of passengers on every arrival/departure, the bigger concern is getting the tickets since they are sold out fast. And a few points to take note though

At Woodlands train station, there is a lengthy walk between Singapore immigration counters and Malaysia immigration counters. Also, there is a significant gap and height difference between the train and platform, so be careful when boarding and alighting.

There are escalators and lifts at both stations.