When you mentioned it being your "first time", did you mean this is your first time playing SHIII, or that it's your first time with the stealth meter turned off?
If it's your first time, damn you for knowing far more than I did at the outset! I was firing fish at the sterns of fleeing Coastal Merchants and "hiding" from DD's at periscope depth (hence, I've had the same experience in sinking a DD...except he sunk me too, that time

).