Power up sequence circuitry
There are a variety of supply supervisory ICs designed to help with this task. Check a distributor with parametric search such as Digikey (PMIC supervisor) and the individual manufacturers. One method is a reference with a comparator or window comparator on the first supply followed by a delay to enable the second supply. In simple applications you may be able to use a regulator with a 'power good' output to enable the second supply. Sometimes just having a common source or deriving one supply from another is enough to meet sequencing requirements (but in this case it appears not). Your stated specs may be met with a reset chip such as an ADM809 (reference and comparator and timer) powered from the first supply and enabling the second, but thats far from a sure thing. It's not trivial to design analog circuits from scratch that have guaranteed behavior at any power supply voltage (and any digital circuits will be slave to the quality of analog circuits used to initialize them) and in any dynamic condition (think of brown-outs, power failing or sputtering during startup or shutdown) so I suggest using a canned solution.

One note of caution- do not neglect the power-down requirements, which can be even more demanding to meet. One design I did needed a relatively large capacitance to provide proper power-down sequencing and the start-up had to be delayed until the reservoir was guaranteed to be filled in case power failed during the start-up. If this sounds a bit paranoid, the cost of a possible failure was astronomical so everything recommended was followed absolutely to the letter.