I don’t fly the single Diamonds, but I do fly the twin - a lot. As a fan of the DA62X mod, I can tell you that the author knows how to mod a plane. That said, I don’t know if his DA40 mod will address this particular issue, but it can still make the rest of the experience better.
Comparing the G1000 behaviour with the steam variant of these aircraft is a tad misleading for the following reasons.
Aircraft generally don’t have an avionics switch control the primary flight and engine instruments if they require electrical power. It is generally reserved for the radio stack items primarily as a means to protect them by keeping them turned off during engine start and as a secondary feature to provide a quick and easy way to turn them all on or off. When you apply that to a G1000 aircraft it means the G1000 will power on when the battery master is on. You will note that the radio frequency display areas are missing (red X’d) because the avionics part is not powered yet. Once engine start is completed avionics is switched on and these radio related functions become active.
This is all very general and there will likely be some exceptions to this here and there but it’s the general reason why they may appear different. This is why this is not a bug.