Mustering happens right away for units.
But units mustered will fight at one step lower if forced to fight the same month as they are mustered, as they are yet not fully equiped, trained to work together and so on.
(The unit is called "a Green Unit" while this is so)

As an example, Infantry which usually have a Melee of 4 and a defence of 14, would have a Melee of 3 and Defence of 13, if having to fight before the month is done.
Green makes Melee, Charge, Missile, Defence and Moral bonuses to be one lower. Also for units with Special Abilties, these might be at half affect while Green.

 

Unless otherwise noted, regents who control domains comprised entirely of holdings must convince a province ruler to allow them to raise an army. Mercenary Units can be mustered without anyones approval.

Unit Muster Requirements
Archers Province (2) or Law/Temple/Guild (4)
Cavalry, Md. Province (3)
Engineers Province (5)
Infantry Province (1) or Law/Temple/Guild (4)
Infantry, Elite Province (3)
Irregulars Province (1) or Law/Temple/Guild (3)
Marines Province (3) or Law/Temple/Guild (4)
Knights Province (4) or Temple (5)
Levies Province (1)
Pikemen Province (2) or Law/Temple/Guild (4)
Scouts Province (0) or Guild (2)

At any time in a turn/season (3 months) one can only muster in total the province rating. No matter who does the muster. (Levies comes on top of this, but the order is levies, then a total of muster of the remaining province rating).

For the sake of Ships, Mustering is not immidiate, as they will have to be built. If you buy ships from someone, you get them when they're delivered. But if you build them, you get to build your level of Shipyard GBs per month. Thus larger ships might you many months to complete. You can have Ship Yard Level amount of ships being built at the same time.