I shall give an alternate explanation that I think should be considered. Trimethylamine, the leaving group, is a much stronger base than bromide or iodide alternatives. The effect is the reaction will be less SN1-like. If the rate limiting step requires removal of the more acidic hydrogens (CH3>CH2>CH), that would give a Hoffmann product. You may think of this as somewhere between an E2 and an E1cb elimination.
If a reaction were completely concerted, then the more acidic the hydrogens and the larger the possible collisions, the greater the amount of Hoffmann product one should expect. The Zaitzev product is the result of removal of the least acidic hydrogens. The more SN1-like a reaction is, the more the product will favor a Zaitzev product. In this case, the neighboring intramolecular electrons are donated. They correspond with the more substituted carbon. The participation of those electrons will increase the acidity of the more substituted hydrogens.
This is only a suggestion. Some reactions are dominated by stereoelectronic effects. If the electrons that are anti, e.g., by restricted rotation, will give the predominant product.