Fertilizers should be applied as the directions on the product label state, because different formulations may act differently with regards to how its nutrients are made available to the plant and how they interact with the soil. (Some forms of nutrients need soil microbes to break them down before roots can absorb them, for example, while others are immediately available for root absorption.) Some fertilizer formulations are applied dry to the soil directly (on the surface or mixed-in, it might not matter if the label doesn't specify) and begin to dissolve slowly as soil moisture or heat gradually releases its nutrients. Others must be dissolved in water before being applied so that the concentrated form of dry fertilizer doesn't "burn" the roots on contact.

Plants must absorb their nutrients in dissolved form, so at some point soil moisture is a necessity for root absorption, but whether or not a fertilizer should be applied dry or diluted in water is up to the manufacturer. (You do not need to wet the ground separately before or after fertilizing if the soil around the roots is already moist enough for the plant's health. If a plant is drought-stressed, though, they should be rehydrated with watering before fertilizer is applied so the roots are not stressed.)

Using a mister to spray fertilizer solution onto the soil surface will not adequately deliver enough nutrients to the plant's root zone. (The exceptions would be an orchid whose roots are growing more in open air rather than in a pot with potting mix, or an air plant / Tillandsia or related bromeliad that does not use roots to absorb nutrients.) Whether applied dry or wet (like in a watering can or gallon jug of water), water the soil or potting mix thoroughly with the solution just as you would with normal watering. This ensures enough of the application reaches the entire absorption zone of the roots. Broadcasting fertilizer by hand can be perfectly fine if it's a formulation that is meant to be applied dry, like granular or pelletized products. In this case it's important to pay attention to the dosage rate provided by the manufacturer so it's not over-applied. (Say, a cup of dry fertilizer per 100 square feet of garden bed, or a tablespoon of dry pellets per 10" pot, just to give some arbitrary examples.) A formulation intended to be applied wet (dissolved in a certain volume of water) that is instead applied by hand dry over the soil surface runs the risk of waste (it washes off the soil with rain or irrigation, or blows away), over-dosing some areas (as too much dissolves in once place), and under-dosing other areas that don't get as much product applied.

Miri