Construction bots just build blueprints and deconstruct things marked for deconstruction. They take items from providers first (active then passive) then storage. They'll put things picked up into storage (not sure if they go into requestors directly though).

You can build a personal robo port and put it inside your suit, then robots you have in your personal inventory will construct/deconstruct in an area around you and put/pull from your inventory only.

Usually you'll want more logistics robots than construction but you can select any robo port and see the number of available/idle bots of each type in the network. If you wanna get real fancy you can get these numbers out with wires and use combinatiors to do some logic like: Only add bots if all bots are in use or other such things

Edit: Construction bots will also repair damaged buildings! Just have repair packs in storage in your network somewhere and they'll make sure every building inside your network is at 100% health!