Noise of an amplifier due to power supply current ratings?
The best answer I can give is "maybe".

But first there is an issue that needs to be addressed. It's like this:

If you're not following the manufacturer's instructions, and the unit is not operating properly, you need to start following the manufacturer's instructions before you start complaining.

I am astounded that you don't understand this.

So get a 2 amp power supply and try it. You should have done that before you sent the unit back to the manufacturer, and I wonder if you informed them that you were using an undersized power supply. If not, you were wasting their time.

Of course, when you say, "I tried with different 12V power supplies one was 1A rated I had the same issue," the obvious question is, what were the other supplies rated for? If the 1 amp unit was the beefiest you had, you really were wasting everybody's time.

With that said, a marginal power supply might, under some circumstances, cause something like you've seen, but it requires a pretty delicate balance of being right on the edge of being in current limit. 1 Hz is the sort of frequency that is hard to explain. It's really too slow for most electronic issues, and too fast for thermal, but it's not impossible. It ought to be easy enough to see,  though. Use one of your other 12 volt supplies as a reference, isolate either your scope or your power supplies from AC ground, and look at the amplifier 12 volts. If the power supply is the culprit you'll probably see the same 1 Hz there. And, by the way, if you don't isolate properly you'll probably damage your scope.