When finding an AC adapter for the device, you need to check:
* type of voltage (AC or DC)
* polarity if DC
The first 3 need to match exactly. For the last one, you want the supplied amps to meet or exceed the used amps.
It sounds like you're not quite matching on that last point. It's working because the power supply designers have some amount of "headroom" designed in. So obviously your 1.2 amp adapter is (barely?) able to supply the power the monitor needs.
With power supplies, using too much power typically causes some part to overheat and perhaps eventually fail. It may fail nicely and just shut down, but if it's poorly designed, it can fail badly and send out too much voltage to the monitor and damage it.
Keeping the supply cool might help it last longer. If you feel it being too hot, you should replace it soon with a higher capacity one.