12V 1A, 5V 1A, or 5v to a cheap little power bar does not tell a thing if it is a good power or not.
You should really know the quality of your power supply. Expensive is not always good. Cheap my not be bad at all.
But you must have a way to test your power supply if you think you have power supply issue.
Here are some test i made with how i power my modules:
using original apple charger: not 100 percent good. sometimes, data request is not complete.
using 5V from my wall mount AC adaptor: same as apple charger.
using 5v supply from tp-link router. 100 percent ok.
i have that project for many months now. i started that with a tplink router power supply. never had issue.
just recently, i tried to use the 2 other supplies, and i had issue. took me a while to figure out because i thought the issue was due to updates i constantly do with my firmware. but the small issue, "missing chars on data requested" was related to bad power supply.
I dont have problems now with esp8266 with that power supply set up.
before i used to have a lot of those. there were units i tested that run 100% ok for a week, and after a week, it will start to run crazy and will reboot from time to time.
esp8266 seems really a good chip. i have units running in the industry now.
i just have a feel that the manufacturer still have a lot under their sleeves. well, that seems really obvious.