VMware snapshots can be done in two ways.
One way involves VMware telling the VMware Tools instance in the guest virtual machine to use a shadow writer to freeze I/O to the virtual disk so VMware can take a consistent or "quiesed" snapshot.
You also have the option of NOT using the VMware Tools instance to initiate a guest-side quiescing of the file system, this results in a crash-consistent backup. It would be like yanking the power cord out of a server while running - it'll most likely come up fine but there is a greater chance that data is lost or corrupt.
In some cases the application simply cannot tolerate a shadow copy operation on the file system, I have seen this before many times. Yes, you get a good backup, but you crash the application in the process. Custom apps are the worst for this.
As soon as the snapshot is taken, regardless of type, Veeam backs up the snapshot to its backup target. Once the copy of the snapshot is made, Veeam deletes the VMware snapshot (consolidating the VMDK with the delta changes that occurred during the backup operation). This is pretty normal as far as VMware backups go.
Quiescing the file system prior to taking a snapshot is the best way to go unless there is a specific requirement not to do so. The best place to look for details on this would be on VMware's web site as they have multiple KBs on working with snapshots.