The pesticides don't work - why biological controls are best for fighting pests
Pests are really good at what they do, they have evolved to evade attack from predators and this serves them well for sprays too.
They hide in the parts of the plant you can't get to with a spray or they simply are resistant to the spray if it has been used over a period of time.
What if I have sprayed, can I still use predators?
Yes, but you will have to wait a while. Consult the bottle or seller of the spray you have used (this goes for neem and other 'natural' products too), look for where it tells you how long it will protect the plant for. It may not say this but it might tell you when you will need to repeat the application. Either of these timings is giving you how long the poison is still on the plant, so how long it goes on killing insects (not just the pest) after it has been applied.
After this time it should be safe to set your small army of good bugs free to clean up your pest problem.
NB - Do not order live predators in advance, they should be used as soon as they arrive. If you have already ordered just ask for shipping to be put back.