How does Atk Tactic and the other Tactic skills work?

The tactic buffs are used only for mixed teams. For example, the buff will apply if the allies, including unit, have 2 or less of the same type (infantry, armored, calvary, etc.) If theres more than 2 of the same type, then the buff wont apply at all, unless theres a different type beside the 3 same ones.

Hero#1--Horse
Hero#2--Horse
Hero#3-- Infantry
Hero#4--Armor w/Tactic skill

since in the team there is only 2 or less unit with the same movement(in any combination), the units the around 2 spaces of #4 will get the buff

If I'm not mistaken, it's not as all-or-nothing as it seems either. If you had three infantry units (one of whom has Tactic) but one cavalry unit, that cavalry unit should receive the Tactic buff, just not the other infantry units.

It only work in mixed teams.

For example, horse cavalry won't activate it, but 2 horse and 2 infantry will do it. If you use it in 3 horses and 1 infantry, the buff only affects infantry, cause the number of horses is more than 2.

I learnt this before when I want to use Eirika. Apparently, tactics are core to her