When I connect more than 1 digitization chest with the logistics option turned on it starts constantly outputting items from the Storage.
For example I set a constant combinator signal of 100 iron plates and connect it to 1 chest, It pulls 100 iron plates from the Storage to the chest as expected.
But then I connect another wire from the same constant combinator to another chest and it starts pulling iron plates from storage to both chests, first 100 at a time then 200 and it keeps going until it fills the chests.
Is this a bug or is it intended behavior?

I cant check right now but it sounds like The Digitization Chests allow the "Read Contents" Circuit Option. Meaning when you have that on, The Chests not only get the Constant Combinator Signal of 100 Iron but the Second chest also gets 100 Iron + 100 Iron of Content from the already filled chest. That in turn then starts an infinite Cycle as Digitization Chests always try to fulfill all Signals not just Constant Combinator ones.

I thought that was the case when I chained the signal from one chest to the other, but it also happens when each chest is connected directly to the constant combinator and dont have any signals connected to each other.
However it doesnt happen when I connect one chest with the red wire and the other with the green.

When connecting both Chests via the same Wire color to the same Combinator you are still connecting both chests with each other. Just check if the UI of the Digitization Chests has the "Read Contents" Checkbox. If so just turn it off. That should fix it altogether.

Yeah, you're right that solved it. Thanks for the help.
I forgot that constant combinators also receive signals, not just send them.

Yeah no Problem, I had the same issue in my run. :)