You could try to make use of events that can be registered on the task server, one of them is claim event that is fired immediately after claim operation so once received you can consider this time as when user took the task. Here is a bit of code that should do just that:
EventKey key = new TaskEventKey(TaskClaimedEvent.class, taskId );
BlockingEventResponseHandler handler = new BlockingEventResponseHandler();
client.registerForEvent( key, false, handler );
// after event has been generated
Payload payload = handler.getPayload();
TaskUserEvent event = ( TaskUserEvent ) payload.get();
This works exactly the same as completing user task where HT handlers register for TaskCompleteEvent. So you need to keep the handler alive to receive that events.
HTH