All policies are configured for a monthly full backups to tape and daily differential incremental backups to DSU.

For NDMP, if you are aiming to use differential instead of cumulative for all your incrementals, then you should do weekly fulls and daily differentials in between.

Or is it incrementing each day up to level 9 and then having a fit? Does this mean I can’t do daily incrementals for more than 9 days in a row?

Since NDMP backup level never goes higher than 9, this means incrementals 1 to 9 will act like proper differentials as you would expect them to be, but starting from the 10th incremental, all further incrementals will still use level 9 which means they will all act as cumulative incrementals referencing the 8th incremental backup.
Things could become confusing, that's why it is recommended to do weekly fulls (level 0) instead of monthly fulls.

This happens in multiple policies on multiple occasions, but apparently not consistently. It appears to act like a cumulative rather than incremental…

My explanation above explains why this is so.

Also, since you have multiple NDMP policies, please beware of the following from the Nbu NDMP guide:

Do not perform incremental backups of the same NDMP data from two different policies.
Incremental backups performed by one of the policies may be incomplete, because NDMP filers perform level-based incrementals instead of time-based incrementals.

Consider the following example:
Policy A does a full backup of /vol/vol1 (level 0).
Policy B then does a full backup of /vol/vol1 (level 0).
The filer now considers the policy B backup to be the last full (level 0) backup of /vol/vol1.
Policy A does an incremental backup of /vol/vol1 (level 1).
The policy A incremental backup captures only the data that changed since the full backup that was done by policy B.
The incremental backup misses any changes that occurred between the policy A full backup and the policy B full backup.

I've been attempting to determine if this is something to do with the NDMP levels However, information is rather light on this subject.

For NDMP details, it is probably best to consult NDMP documentations instead of Symantec.
Know that with each successive run of the same differential incremental schedule, the NDMP backup level increases by 1 (until it reaches 9).
With cumulative incremental scheduels, the level stays as 1 - So that it will always reference the level 0 (full) backup no matter how many iterations it completes. (This is also why cumulatives do not have that weekly full recommendation; you can cumulate to your heart's content if you want...)

NDMP backup levels and backup schedules work like this:
A full schedule on Saturday and a cumulative schedule for Sunday to Friday would mean weekly full (level 0) and daily cumulative (level 1).

A full schedule on Saturday and a differential schedule for Sunday to Friday would mean weekly full (level 0) and daily differential (levels 1 to 6).
NetBackup will automatically do level 1 on Sunday, level 2 on Monday, and so on, until it reaches level 6 on Friday, then the next backup on Saturday will be level 0 again (full). Then the cycle begins again.