Why does there's one the AC DC adapter that has the ON (ready) led intermittently being off-on when the digital MM is probing its output on Ampere measurement, while on DC volt measurement it gives as normally well as it's supposed to be ?
This adapter has specs

input 100-240 V AC 600 mA
output DC
15 V 500 mA
32 V 375 mA

would there be faulty function inside it or
this indication is reasonable for that adapter circuit spec (can't be inspected inside yet as there's no screw at all to open its box up)?

 

led intermittently being off-on when the digital MM is probing its output on Ampere measurement

How you "probing its output"?
If one of the ammeter terminals is connected to ground, it's not surprising the LED is blinking, since that shorts the output to ground.
An ammeter must be put in series with the output and a load.

 

You cannot probe with a meter in ampere setting.
You will end up blowing your meter, a fuse, or something costly.

 

Just adding to the excellent replies above. The "mA" statements on the plate of the power supply indicate the maximum current output it can provide before an internal protection circuitry actuates and powers down the output - either in case of overload or a short circuit scenario (which seems to be your case)

Since the LED is probably tied to the output, you will see it correctly turn off. In addition, the protection circuitry might try to turn on the output at a given interval and probe to see if the short circuit is removed. Since you still have your meter probes tied to it, the output is powered off continuously.