Right, but the triggers get a little weird unless the screw is easily turned by hand, I.e. not even remotely snug.
When the set trigger is pulled, the front has a “click” takeup almost like a two stage trigger, and the set trigger (rear) also clicks when squeezing it. This doesn’t happen when the lock screw is loosened. I tried adjusting the trigger set screw and it didn’t do anything to fix the issue. maybe this has to do with the new tumbler?
Like the others said, the side plate doesn't need to be tightened down using very much force. After all, it is the wood lock mortise that keeps the lock in place and prevents its moving.
There is nothing on the tumbler that touches any part of the set triggers, set or unset. The set trigger assembly is a unit by itself and the only part of it that touches the lock is the blades on the top of the triggers. These make contact with the sear arm on the lock and when the trigger is pulled, they push the sear arm upward, disengaging it from the notch on the tumbler.
When the rear trigger is pulled against its spring load, it is moving a blade with a "catch" on it to a position that will engage the latch that's built into the front trigger. When the two mesh and lock up, it makes a "click" sound. That is normal. I'd be concerned if I didn't hear the faint click sound.