..despite living here 40+ years. We have a south facing oleander. I posted here last summer asking for advice after it got cooked by the heat. Thanks for the replies.

Well, it's doing a lot better and starting to sprout after pruning the dead branches a while back. On a side note, it's never really bloomed well, just a few flowers. I looked at it a few days ago, and there were orange dots near all the new growth and flower buds.

Researched it and found out they're oleander aphids (Aphis nerii). They also attack plants of the milkweed family. Folks grow those to attract monarch butterflies and are hesitant to use pesticides because they don't want to harm the caterpillars. I went nuclear on them, though. Plain old Raid does the job. I hope this can help someone.

Pic (not mine) below. Slightly smaller than a pinhead, and appears more sphere-like. I live in a suburb of PHX.

It has been my experience that you can never get rid of them for good, they just keep coming back.
I spray them several times a year.

I get them on only one of my many of adeniums, that one must be very sweet to attract them. I use insecticidal soap that you can buy at any nursery or hardware store, or you can make your own.

Many landscapers have switch from oleander to other hedges because of these pest.  We use green hopseed, ficus or sour orange for hedges to address these pest.  I also regularly remove oleander when doing remodels for the same reason.