I know that heat exchange machine is capable of brew & steam at the same time, my question is do I have to wait for the heat light to go off before I pull the shot? I used to own a silvia and that one requires me to wait before the light to go off before pulling the shot.

I'm not sure how the Oscar is designed to operate but..without a bit more info from you, it's tough to accurately answer your question.

IF you are asking about turning the machine ON from a cold start and pulling a shot after the heat light has gone out, you are very likely going to get a result that isn't 'optimal'. The grouphead, portafilter and pipes should all be warmed up roughly 30 minutes after you first turn your machine ON. This is also a great time to bleed any false pressure in case your machine requires that too.

IF your machine has been on for at least 30 minutes, and the false pressure has been bled, AND the heater light has cycled ON and OFF a couple of times, then most heat exchanger type machines require a short flush of water from the group (not the hot water tap if so equiped) until the 'hissing/popping/crackling' is done. Generally, at that point, the water has 'cooled' down to an appropriate temperature to pull a shot without 'burning' the grounds. This should put you close to the correct temp for pulling the shot.

What would help you tremendously would be a styrofoam cup and a thermometer capable of reading up to around 210 degrees F or around 100 degrees C.

I recommend you have a look at the HOW-TOS at the top of the screen and in particular, this thread:
Managing the Brew Temperature of HX Espresso Machines

I apologize if I have misunderstood your question.

Short answer is no, you don't. Your Silvia is a single boiler with boiler temp fluctuations due to heating element cycles (water is drawn from a boiler where it is heated by the heating element). The Oscar is a heatexchanger where the water is flash heated on the way as it passes through a pipe in the boiler. The "temp variation" you need to worry about with a heatexchanger is the super heated water thats been sitting in the pipe during idle. Once you flush that out (see above article) at the beginning of your session, you will be at right temperature and don't need to temp surf (assuming all settings are correct etc.)

Mystery solved, thank you for your advice.