Is it safe to use the same cooking utensils for raw and cooked meat?
Personally, cooking for myself, I would only worry about it if were something more likely to be harboring pathogens, such as chicken. When doing steak, I just rinse them in hot water.

If you're worried about it, you could soak the spatula or tongs (the part that came in contact with the raw meat, obviously) in some boiling or near-boiling water for a few seconds, long enough to get them to 160°F+.