There were no intentional changes to the engine logic or any control assignments in v1.2a, as it was only a very small update to cover a handful of items noticed post the larger v1.2 update: https://support.justflight.com/en/support/solutions/articles/17000152601-f70-f100-professional-changelog
From my experience, engine start issues that only affect some users are almost always related to a control assignment/hardware conflict.
The easiest way to test that is to temporarily unplug your flight sim hardware from your PC (joysticks, throttle quadrants, etc.) and then try to start the engines using the same method as previously. If the engines start with no hardware plugged in, then that suggests a control assignment conflict, and I recommend checking that FUEL VALVE, STARTER, MIXTURE or PROPELLER assignments are not unknowingly assigned to your hardware.
If that doesn't resolve the issues, then it could be something else, such as another mod/product causing a conflict. In any case, Just Flight Support will be best positioned to offer further assistance.
Mark - Just Flight