It depends on the aircraft (and conditions). In some aircraft like the MD-11, the deployment of ground spoilers causes a nose up pitching moment- in such a case, the spoilers should be deployed after nose landing gear touches down.
An example is the incident in Hawaii where the aircraft, a MD-11 exhibited a pitch up tendency during landing and the pilot had to initiate a go around. The factual report noted:
The MD-11 Flight Crew Operating Manual, Volume II, Landing Roll Procedure, contains the following note:
Ground spoiler deployment causes nose up pitching moment. This effect is most noticeable at aft centers of gravity. It is important to check the nose up pitching tendency with forward pressure on the control column and smoothly lower the nose wheel to the runway.
In some cases the deployment of thrust reversers could also have similar effect. In such cases, the thrust reversers and spoilers should be deployed after the nose wheel touches the ground, while in other cases, it is done after the main landing gear touches down and before the nose gear touches down. From FAA Airplane Flying Handbook:
... some airplanes tend to pitch noseup when reverse is selected on landing and this effect, particularly when combined with the noseup pitch effect from the spoilers, can cause the airplane to leave the ground again momentarily. On these types, the airplane must be firmly on the ground with the nosewheel down, before reverse is selected.
Other types of airplanes have no change in pitch, and reverse idle may be selected after the main gear is down and before the nosewheel is down.
There are other issues as well- deployment of thrust reversers before the nose wheel touches the ground means the pilot may not have sufficient authority for steering the aircraft in case one of them doesn't deploy. To prevent this some aircraft restrict the use of full reverse thrust till the nose landing gear is on ground (though idle reverse is permitted once the main gear touches down).
Also, for aircraft having engines in rear, the deployment of clamshell type thrust reversers can have clearance and debris ingestion issues which can limit their deployment. Also, the effect of spoiler deployment on the aircraft aerodynamics has also to be considered. For example, Boeing states:
The MD-80 and MD-90 in-flight spoiler lockout mechanism prevents the undesirable flight control configuration of deployed spoilers in either the speed brake or ground spoiler mode when flaps are extended.
There are also other aircraft (like Tu-154) where the thrust reversers were deployed before touchdown. So, all in all, it is better to consult the particular aircraft manual to decide when the spoilers/thrust reversers are to be engaged.