It is spasticity. Stretching is very important. I have this problem in the mornings, and it causes me to have a little foot drop (I stub my toe on the floor.) I stretch out my calf, and then do the hurdler's stretch for my hip flexor muscle.
Hey it sounds to me like it might be something like spasticity, though it could be something a lot simpler. If you think of runners or the like, calf muscle get tight from use, when running or walking etc and its why stretching is so important before and after they train.
A few things to concider, what were you doing prior to sitting down for awhile, is it possibly the prior activity and not the sitting thats causing it? Are you totally unable to walk heel down or are you not able to because your avoiding the pain and discomfort of heel down? Do you stretch at all? When you sit are your feet flat to the floor or are you on toes? Do you have upper leg muscle weakness so the calves are doing more of the work?
You might try stretching your calves before you sit down and then again before you walk after sitting down, it might help to keep doing basic stretches through out the day.
Cheers.......JJ