Some testing has made me determine that since Processed fuel is using a custom fuel category "processed-chemical", it isn't properly detected by this mod as a fuel burner type buildings/inserters can be inserted to. when I changed it's category to "chemical" as vanilla coal is, it began outputting the processed fuel into things like furnaces.
It seems odd that they would have done this, but it seems there is an actual reason.
The Fuel processor that makes it accepts any "chemical" fuel items, and converts a total of 10MW of this fuel in order to make 1 of the processed fuels. Had the processed fuels been configured as a "chemical" fuel, then it would be possible to insert the output back into the input for infinite pollution with no gains, and that seems like why it was made to be like this...
That being said, I believe a way to add the compatability would be to add a check for this mod, and then to append the custom category to the code that inserts the regular "chemical" fuels.