Remember, this only comes into play on tied contracts, which in most cases means max contracts. Otherwise, the 50-win team can sign anyone he wants as long as he offers $1 more. And they don't eliminate the previous season's record because it IS a tiebreaker, per this quote from the updates thread:
"The tiebreakers are as follows: Playoff contention (based on last seasons winning %), coaching staff, and ballpark."
Actually, that quote even lists them in the order that makes sense, to me. I've never read anywhere that coaching staff comes before record, which was why I was wondering where the assertion that coaching staff came second came from.