"Tactical" is also an Army adverb describing things that are done in the field on exercises or in combat, as opposed to strategic things that are done at long distance or for organizations higher up the food chain than the corps. It can be a term of praise; someone who always knows what to do and when in the field will be referred to as "fucking tactical" or in extreme cases, "fucking hardcore tactical", although one usually only heard that in reference to Rangers, Green Beanies, and other species of snake-eaters.
As applied to ASA units, tactical indicates units that are either in direct support of maneuver units (for example, the 340th ASA Company (Regimental Support) assigned to the 11th Armored Cavalry Regiment) or general support of such units, such as the 331st ASA Company (Ops Forward). These units would receive tasking from the division G-2 staff or regimental S-2. Strategic units, such as Field Station Berlin, received tasking from NSA at Fort Meade and were generally uninterested in tactical intelligence.