I finally started playing Dynasty Warriors (8 on PC) and I'm very confused on what I should do in the battlefield
I'm doing story mode, and basically I go from objective to objective, ignoring my teammates, people keep telling me that the game is very tactical so I think I'm missing something.
DW7 and 8 are very linear. They minimized the effects of controlling keeps, so, yeah, you don't need to take care of your team most of the time. Just follow the objectives. There are also some optional objectives that can change events and eventually unlock a 2nd ending for each story.
You're also likely playing on normal, which has very weak enemy officers (Hard in DW8 does seem to assume that you have some weapons already though, so I wouldn't recommend starting there before you get some better weapons), so you get enemies that don't really threaten your troops most of the time (so you don't need to go back to rescue them unless it's part of the story progression).
How can I order the NPCs to go help units under attack?
You can only give orders to NPC units in the Empire games (or the recent Samurai Warriors titles, but there it's only for the 2/4 party members you choose at the start of the level).
Generally, when people mention tactics in Warriors titles, it's more about prioritizing different objectives and/or map control (with the bases that spawn more troops for either your army or the enemies), like choosing between advancing to a goal or retreating to help your army take care of some enemy officers that are advancing towards your main base.
There are also the keeps/bases around the map that produce troops for either army, conquering them also usually gives a moral bonus that makes the army in general fight better. However, bases are almost irrelevant in DW7 and 8 outside of the Empires titles. They don't seem to produce troops anymore and the moral is much more heavily weighted by the story events than keeps you conquer. Some recent titles that keep bases important, aside from Empires (which doesn't have a story mode at all), are the DW Gundam ones and Hyrule Warriors.