I'm less concerned with whether it was mentioned in writing than that it was mentioned at all. Given that it was, and given that it is paid time, IMO you are actively employed through to the 14th (in the example).
However, just for future reference, this could VERY easily have gone the other way. If at some point in future you are close to vesting a benefit at the time you are ready to resign, you should most likely wait until AFTER you have vested before you give your notice. You lucked out this time but had events gone differently, it could easily have been that your last day of active employment was Feb. 4.

