I have managed to solve this for myself on the PC. It now works! I can have puppet and delusion at the same time.
To fix this:
Navigate to your folder: C:\Users\<User Name>\Documents\The Witcher 3
Open the file "input.settings"
Find all the entries for "IK_Q=(Action=CastSignHold,State=Duration,IdleTime=0.2)"
Change the entry to have an IdleTime of 0.01. So after your change it should look like this:
"IK_Q=(Action=CastSignHold,State=Duration,IdleTime=0.01)"
There are multiple entries of this setting, so you will have to change them all.
I didn't test it with other signs as this is a universal change to all alternate sign modes. But I am just happy to be able to use puppet and delusion at the same time now. It was driving me crazy to have to choose between them.