Sadly the first circle is not self-reinforcing (and, sadly, the second cycle is entirely accurate).
Instead, in the 'good exurban schools' case, the evolution usually goes:
1. Rural, periphery area attracts affluent folks seeking bigger houses on cheaper land. High-end residential subdivisions are developed.
2. Increased tax revenue allows for good schools, nice government amenities.
3. Good schools attract additional residents. Residential population swells, commercial and industrial population remains low.
4. Residential brings fewer tax dollars per infrastructure cost than commercial or industrial. At some point, municipal costs (roads, sewer, fire, schools) begin to approach revenue. Services are cut. Schools decline, making residents eligible to contemplate moving to another area in step #1 or step #3. Those who can't afford to move to a newer area stay; they are thus on average lower-income than those who left. At this point, there is a danger of falling into the second cycle.