When we build our Loft Conversions we always insert the staircase last.
By doing this we create much less mess in the property below and we access the working area via the scaffolding. The use of dust sheets over doors and halls is also required to minimise disruption. Ask the builders if this is an option.
However there will still be some mess.
If you do need to move out while the conversion is under way then you will have to ask your builders regarding the time they will take to complete, usually 6 to 8 weeks.