Why would an IC have a minimum power supply rise time?
During Power On Reset, there is a special analog circuit that detects the VDD change and decides to reset the processor. If the change on VDD is not fast enough, the POR circuit could decide that it is not a real power up event and leave the processor unresetted. Starting a digital machine with no reset is prone to all kinds of failures since the internal registers and volatile memories start with garbage contents. And as it is well known, garbage-in produces garbage out.