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"Compete" doesn't necesarily mean that a player is guaranteed a spot if they have a good spring training. When you are dealing with someone who has never played professionally and the alternative is an extremely experienced player who has proven himself at the highest level, the standard is not the same for the two of them. Hultzen might be better than Millwood out of the gate, but there are a bunch of legitimate reasons to go with Millwood to start the year if he looks like he still has something left.
If Millwood looked terrible, then Hultzen likely would have had a real shot at making the club immediately, which is what Jack meant by "compete".