Timing is critical because the UE can move different distances from the base station, and LTE requires microsecond level precision; the speed-of-light propagation delay alone can cause enough change to cause a collision or a timing problem if it is not maintained.
There are two forms of the RACH procedure: Contention-based, which can apply to all four events above, and noncontention based, which applies to only handover and DL data arrival. The difference is whether or not there is a possibility for failure using an overlapping RACH preamble.