It doesn't explain the timing. If Spurs had intimated to him that they'll sign him in January, it wouldn't have been halfway through a Chelsea medical with one hour to go on deadline day and, even if they had done that, his agent wouldn't risk his clients' entire future on a frantic last gasp verbal exchange with little time to consider the implications.
It is very unlikely in my view that that is what has happened. If Spurs had tapped him up, they did it a long time before now and it would have meant no medical at Chelsea this evening. Because there'd be no point - there's nothing to gain from having discussions with Chelsea to that extent in that scenario, because 'tapping up' means arranging an outcome well in advance of time and that would have meant Barkley and his agent rejecting a move to Chelsea out of hand.