Mark,
Its normal to do so as you describe. To reset the fly, the hammer must drop past the half-cock position, and an upright frizzen will impede the progress of lowering the hammer.
So, the frizzen should be pushed fully forward, exposing the pan. If the frizzen is half-way between fully upright & fully forward, there is always a chance of an accidental discharge. By extending the frizzen fully forward, you put yourself in a much safer position when grabbing the hammer to lower it.
You certainly don't want to have the frizzen upright when trying to take the hammer out of the half-cock position on the tumbler.
Keeping the muzzle pointed in a safe direction isn't always uppermost in our minds when we're working with the lock. Obviously, when the barrel is horizontal, it presents a danger to anyone facing it.
Some folks slip a leather "boot" over the frizzen, AKA frizzen cover, to add to the safety of the shooter. The cover has a leather thong on top and is attached to the trigger-guard to keep it handy.
You're doing the right thing.
Keep 'em in the center, close together.