I created a VM with premiums storage (DS), but my existing VHD I created it from was on a standard disk. Is this VM still considered premium performance even though the disk says Standard where the VHD is located for this new VM?
DS-series VMs are capable of using Premium disks for either OS or Data (or both). But the performance will ultimately depend on which type of disk you use. If you use a standard disk, it will perform just like a D-series.
In your case, since you created your OS disk as a standard storage VHD, it will have all the performance characteristics of standard storage. Depending on where you're storing your data, that may or may not impact you (e.g. if you have Premium data disks for, say, your database files, you'd then have those disks running at one of the three Premium disk performance levels).