Yes, I think it's normal. Yorkies were bred to be used as ratters afterall
. Their job was to flush out and kill vermin. Some instincts just don't die out even though we wish they would. My Rasta, all 2 lbs of him killed a grass snake then decided to roll on the body
. Your yorkie probably shook it really hard causing it to break it's neck if you didnt see any broken skin. I don't know about the tie out. Depending on your area I probably wouldn't use one. We have hawks, vultures, and owls here so I know I wouldn't. Are there any chipmunk/squirrel deterrents to keep them out of your yard?