You get what you pay for (if you are lucky). You say "very clean" at $8 ??? you could have a measure of start up control by having a relay powered by one line switching the other lines on, or even two relays, so +5 first, then + 12V then - 12V.
Frank
Hi
If you will low current its easy.
you can use lm7815 & lm7915 & lm7805 .
but for more currents i suggest you to use smps such az lm2576 series.(3amp)
and for currents more than this you can the other smps circuits such a buck,boost, flyback ,forward ...
No basic problem. But you should choose regulated ones. If you draw less than the maximum rated current from an unregulated wall wart the output voltage will be higher than the stated figure.
I guess the above solution wouldn't provide any protections or controlled startup conditions a nice Triple output supply would?