The mobile platform carries an on-premises requirement: destruction happens at the customer's premises. The audit checks that the provider's written procedures call for mobile work to be done at the customer's site unless the customer has agreed otherwise in writing. That exception is yours to control. Read the service agreement for any clause that permits destruction elsewhere, and state in your own contract that all destruction is completed at your address.
The manual's glossary describes a mobile operation as commercial-grade destruction equipment working inside an enclosed, securable truck or trailer at the customer's site. A provider that collects drives at your office and shreds them at its plant is doing facility-based work with a transport leg in front of it. The facility line of the certificate is the one that applies to that job, even when the quote calls the pickup onsite.
The hard-drive endorsement adds requirements for records. Before the job, the provider gives you a written description of how it destroys the drives. It records the serial number of every drive and returns the log when the service is complete, unless you've signed an opt-out agreement. The drives have to be damaged until the "platters will not engage." The solid-state endorsement follows the same pattern with two differences. Serial numbers are recorded "where possible," and the device has to be damaged until it can't be used.
That wording leaves two things to your contract. Neither endorsement sets a particle size for drives, so a shred dimension in your policy belongs in the agreement with the provider. And "where possible" leaves room for a solid-state drive with no readable serial number to be logged without one. Record the laptop's serial number or asset tag beside each solid-state drive in your inventory, and ask the provider to log that identifier when the drive has none.