Adrenaline from the recent muscle memory of fighting plus the adrenaline of exploring a curious situation cause Tonks to keep a tight grip on her wand that, while not in position to take the offense, could be easily turned to do whatever it was that she might need to do.
But wands didn't help with moments that dropped one's jaw to the floor. She didn't respond with her name yet, only partially out of caution. Her look was open surprise as she studied the wizard across from her.
"Hullo," she began tentatively. "Regulus..Black?" As a child, Tonks had never met her other second cousin; he had been one of the people that pretended Andromeda didn't exist anymore. And as an adult..well, he had been dead long before she reached her adult years.
If it weren't for a small portrait she had found by sheer chance at Grimmauld, Tonks might not have even known what he looked like at all.
"I think I hit my head earlier." Or had gone mad and occupied a bed near the poor Longbottoms.