The most layered tips I installed are far more constistent from the first hit on like single layered. From my personal experience I would compare the tiger emerald partly to an average / good lepro. The emeralds very often have more mushrooming than other multilayerd tips, and they hold their shape not so well. So I know that the emeralds should be pressed, but only pressed, without soaking them.
After pressing an emerald or compressing it well after glueing, it behaves like most other multi layered tip: much less change in hardness than single layered and few or no mushrooming. But also at most multilayered tips you con see the same effect principally like scdiveteam desribed it (very good desription!) in the 2nd post of this thread. But the range of hardness' change is much smaller.
And if you choose a very high quality multi layered tip like the kamuis or some other brands, you have nearly no change in the tip's behavior from start to end.But this is only my limited experience because there are some multilayered tips that I haven't installed or played yet.