@jacob letoile and
@Dalmat - both offered good advice.
@Lobaeux - those white specs look like whitefly to me
If you use the non-toxic ''safe'' sprays, like horticultural oil, soapy water, water & milk mix, or any of the other home brews, you really need to keep repeating application every few days to catch the new hatchlings from eggs laid by the previous generation. Keep spraying a couple cycles AFTER you no longer see pests.
If you are going to use a pesticide - remember, it is a highly regulated group of chemicals. Technically the labels on the pesticides carry the weight of law, and what is on the label is the limit to how it is used. There is no way around it. You need to take the time to read the labels, both before you buy, and before you spray. If a pest is not listed on the label, the pesticide will not kill that pest. This also means you really need to know what the identity of your pest is. An insecticide for mealy bug, will not kill spider mites. A pesticide for spider mites will not kill mealy bugs. The target pest MUST be listed on the label or you are wasting your money and time. Finally, you really need to read the safety precautions and wear the gear the label recommends. Also, the abbreviation REI stands for Re-Entry Interval - this is how long before you may come in contact with the trees you sprayed, or how long you have to keep the kids, pets and yourself from touching the trees. So READ, READ, READ the labels. All the inside pages. A person considered a ''professional'' can be sued for using a pesticide in a manner not itemized on the label. It is vague as to whether a hobby or home owner can be sued, but the point is, the label directions must be followed.
And to get a pesticide to work, you need to follow directions. Too dilute from label recommended concentration, and the spray will merely create a resistant strain of the bug. Too strong a concentration and you may damage the plants. Just as critical, read the label for how often to repeat applications. Repeat at recommended intervals, not a day later, so that the target pest does not have time to lay eggs. Continue to spray at least one or two intervals after you no longer see the target pest. You want to make sure you don't leave behind a residual population.
Finally, in places like Florida, if you are near any of the agricultural areas, the pest you get may be from a population that is resistant to one pesticide or another. On the label it should list a number for Mode Of Action group. If the spray you used did not seem to make a serious dent in the bug population, look for a different pesticide that lists your target pest and is in a different Mode of Action Group. For example, Malathion is an Organophosphate, which disrupts the nervous system of true insects, but largely ineffective with arachnids. Merit is a neonicotinoid, which has a different mode of action group, targets a different system in the insects body. Mavrik, Decathalon, and several others are Pyrethroid compounds, and will have a different MOA number than the previous two. If you alternate between Mavrik, & Decathalon you will be in the same MOA group and won't get any benefit from doing the alternation. Staying inside one MOA group you can develop a resistant population.
Lastly, If one plant on your bench is infected, assume all on the bench have at least a low level population of bugs. Spray everything in the vicinity. If you just spray the plant that is obviously infected, but not its neighbors, the bugs hiding on the neighbors will simply recolonize the weak plant once the pesticide has worn off from your spray.
A lot to take in. I know, but there is no way to avoid it.
Note: I did not specify any particular spray, they all have their place, and what I can get here might not be something you can get in your state.
And if you can not find a pesticide you think you need, check out
http://www.hummert.com/ they will sell pesticides through the mail. I do get some of the harder to find stuff here. Not necessarily the cheapest, but they are an ''honest business''. you can count on good service. If you have a tax ID you can set up a wholesale account fairly easily.