Think of it this way. If the fielder drops the ball while tagging the runner or base, did he have possession of the ball? The answer would be "no". If he drops it after the tag is complete (meaning the act of tagging is complete and the fielder is no longer in contact with the runner or base, or all action has stopped and the fielder still has secure possession), then he had secure possession during the tag.

Remember this, a tag is not complete the moment the fielder touches the runner or base. It is complete when he is no longer touching the runner or base. Or, he still has secure possession at the time action has stopped. To imagine or see all nuances to this requires experience on the field.