James08, magnetization has some time dependence because of eddy currents in the material being magnetized. What happens is that when a changing magnetizing field is applied to a ferromagnetic material, it will induce eddy currents which (according to Lenz's law) produce a field which opposes the original change in field. As the magnetizing field stabilizes to a steady value, the eddy currents reduce and full magnetization can be achieved.
The practical result is that the ferromagnetic material will magnetize fully at its surface first, and with time the magnetization penetrates to centre. This may take several milli-seconds, according to the electrical conductivity of the material. Laminated materials and non-conductive materials such as soft-ferrites can be magnetized at a much faster rate.
The phenomonon causes problems when magnetizing rare earth magnets. These require very high magnetizing forces which are usually provided by high current pulses in the magnetizing coil (kA magnitude, usually supplied by capacitor discharge). The problem is, because of the eddy current it takes a finite time for the field to penetrate to the centre of the magnet hence the pulse must be of sufficient duration, which requires more capacitors. Time-stepping finite element analysis is used in more demanding applications for magnetizing fixtures.
In your application you say you also have other metals (non ferrous?) around the ferromagnetic material. Unfortunately, these will also have eddy currents in them depending on how conductive they are, and these currents will oppose the original field whilst it is changing in magnetude. This is the principle of electromagnetic screening. In effect the system responds like a low-pass filter, the higher the conductivity of the components in the field, the lower the roll-off frequency.