Do you have the File Tree View open and see the Explorer tab? Yes! And do you see also the labels of the drives? Yes! What do you think from where the drive labels are read?

Joking apart. Open
Advanced - Configuration - Application Layout - File Tree View and
- uncheck setting Show volume labels in Explorer view,
- uncheck setting Show registered file type icons in Explorer view (not really needed to avoid access of other drives, but reduces the number of file system accesses a lot),
- uncheck setting Scan for empty folders in Explorer view.
For the other settings in this configuration dialog you have to make your choice according to your needs.
Please note that I don't really know if this is already enough to stop UltraEdit accessing all drives on startup. Perhaps it is also important that the Explorer tab of File Tree View is not the active tab or the File Tree View must be made hidden or even completely closed on startup.
If nothing helps, I suggest to contact IDM support by email and ask what to do to avoid disk accesses on all drives or write for an improvement.
I have reported already by email to IDM that I can hear
sometimes on startup of UltraEdit that floppy disk drive in my old desktop computer at work is accessed. Interesting is that I could whether with old File Monitor nor with Process Monitor of Sysinternals see that uedit32.exe really accesses the floppy disk drive. It is mysterious for me why I can sometimes hear and also see on the floppy drive LED that the floppy drive is accessed, but both file system monitoring applications usually really recording all disk accesses do not contain any line showing me who accesses the floppy drive and how.