That will be the case: I will put 5 decades of decoupling caps on the power lines: 10 nF, 100 nF, 1 µF, 10 µF and 100 µF close to each chip and a bulk cap of 1000 µF directly after the power regulator, which is a linear LDO regulator (+ 100 nF everywhere where usually needed)
Besides, in the Github project mentionned above, a clock speed of "only" 1 MHz is used. The MAX6954 can go as high as 26 MHz. Which is why I find it so weird that he is having trouble. On the other hand, he doesn't use a PCB but wire-wrapped connections..... I wouldn't have done that, but I'm not blaming anyone, of course: 7 years ago, it wasn't not yet so easy to grab cheap PCB built in small quantities for hobbyists.
In my application, I even don't need to go up to 1 MHz, since there will be no fancy effects.
Has anyone got any experience with that chip ?