During my timing belt replacement, I noticed something which I think is worth mentioning here. As you know, locking pins (two for camshafts and one for crankshaft) are used to lock the engine in exact timing position before removing the old belt. However, it seems that it is not the case because I could still rotate the engine just a very tiny bit clockwise or counterclockwise even with the locking pins inserted in camshaft sprockets and crank pulley. So, the engine was not exactly LOCKED even with pins inserted which means the timing will not be super accurate. If accurate and precise timing is so important, why does the manual recommend using pins which are NOT a press fit?
TL DR: The locking pins are an aid to keep things in place and not meant for precision.
While you'd think it'd need to be exact, it really doesn't need to be. It just has to be exact enough so when you put the belt onto the cogs, everything lines up. If you look at one of the teeth in the belt, they probably (at a guess and depending on which motor) encompass 8-10° of rotation of any single part (cam or crank). As long as the right teeth are aligned with the right cog indentation, everything is fine. They don't have to be completely still to do this for you. In fact a wee bit of movement is probably preferable to aid in getting the belt back onto the gears in the first place. The belt teeth align things together correctly and won't allow them to be out of time so long as the teeth go into the right groove on the pulley.
Regardless of how much they move, you should always check to ensure timing is accurate prior to starting the engine (actually, prior to even putting the rest of the engine together). This will ensure you've put it back together correctly and everything will work together just fine upon first start.