I worked in service station as a kid out of high school, the old time mechanics would warn me to never fill a differintial to the plug level when cold, we would fill it so it was about a inch down from the plug cold. I have service many vechicles with hot engine oils, rear ends and trannys, all of them would dump rear end lube out when hot
My message is don't fill it up cold
I use a thin small screwdriver or something similar to check the fluid levels now, I use to use my pinkie finger but that gets old wiping the goo off of your fingers