By precommiting I understand starting to be aware of the fact that my source code will do the particular thing with certainty. Nobody knows his source code completely, and even knowing the source code doesn't imply knowing all its outputs immediately. So, what I wanted to say is that when making the threat, the baron must know that he will certainly act the way he announces (this is the precommitment) and the countess has to know this fact about the baron (this is the signalling part).

Time matters because the baron has to calculate his counterfactual actions (i.e. partly simulate himself) before he can precommit in the sense I understand the word.