In rules for The Tactical Action there is activation sequence:

1) Activate a system
2) Move ships into the system
3) PDS fire
4) Space Battle
5) Planetary Landings
6) Invasion Combat
7) Produce Units

Q: do I need to follow this order or I can for example first produce units, then move some other ships in to another system?

Technically, the decisions you make in moving ships into the system will affect your production, due to fleet supply. Best stick to the activation sequence really.
 

You have to follow the tactical action sequence in order.

Remember, you can do a "transfer action"  too.  

This lets you move ships out of the system you are building in to make room for new ships.  

 New ships can never be built and moved on the same turn. 

Everything in twilight follows the sequences printed on the race sheet.   You are not allowed to deviate from it.

Action cards are designed to override the ordinary rules.  If you want to break a rule, you must try to find an Action card that does that.

Political cards are designed to establish a new rule.  If you want a new rule, you can try to find a Politcal card that does what you want.

Short answer: Yes you must follow the order of play.

 Thanks for the info