Not a disease for burning bush. How long has it been in the ground? If planted only recently, the rootball can either be sopping or too dry. Stick an finger in it to learn which is the case. Same for the spirea. When you plant it, rig temporary shade. If it was fully leaved out when you untangled the roots, it needs considerable time to recover. By the way, also rig shade for the burning nush.

Added zone info. Well, I won't be able to find out (quickly) now by digging. Just had a thunderstorm with rain pouring down all night. Guess I'll see if that helps. The whole plant itself isn't bad. Aside from the brown patches, there is no other obvious issue. No leaves/branch die back. The last couple of weeks has been hot and with clear sun. Just hovering over 30C degree and the location gets full sun from morning to probably 3-5pm. However I have some hydrangea (also new) in the vicinity so I have been forced to water them daily with this heat. I did try to avoid the Burning bush somewhat when watering so it isn't soaked every day. The soil in that spot is decently deep, but hasn't been planted with for probably over a decade. I added alot of compose before planting. Lota cedar mulch, more so on the hydrangea, but should be a good 2" around the burning bush too.

Probably no need to try to control them - it's more a cosmetic issue than a plant health concern. Their numbers appear to fluctuate from year to year, at least on the burning bushes in my own yard. I've noticed lady beetle larvae feeding on them when they're abundant.

I have some flower seeds. I don't have any Japanese maple trees. Too cold up here! What flowers interest you?