Both incident to and split shared are used for PA, NP and CNM (among others). I call these NPP (non-physician practioners). There are also a variety of other abbreviations in common use. Incident to can also be used for other employees, like an RN billing 99211.
Basically, you can always bill under NPP. You WANT to bill under the physician when permitted as you will receive a higher payment. NPP fee schedule is typically 85% of the physician fee schedule.
Each commercial carrier will set their own rules regarding whether or not they follow incident to. Almost all of my contracts specify we will be following Medicare guidelines, so incident to would apply. Your contracts could differ.
For carriers that do not follow incident to, they might credential NPPs and all services should be billed under the NPP (even if it does meet incident to), or might not credential NPPs and instruct you to bill all services under the supervising physician (even if it does not meet incident to).
IF the carrier follows incident to, AND NPP sees patient for ESTABLISHED problem with a documented PLAN of care and the physician is ONSITE, then you may bill NPP services under the physician to receive full reimbursement. Some carriers require using modifier -SA on incident to claims.
I will note for my practice, it is rare that my NPPs are seeing patients when a physician is onsite, and even then it's even more rare that there's no new problem addressed and a documented plan of care. Basically, it's so rare that my billers and coders don't even really look to see if it could possibly be incident to. My NPP services are billed under the NPP.
Here are some references to start your research on incident to billing: