Actually, I don't think it's capable of FIRMWARE upgrades. But it'll do KERNEL upgrades easily.
I believe you're talking about if it's able to upgrade the "core" in the flash cart itself. If so, the DSTTi cannot at this moment. Neither does the R4i or the Acekard 2i (It's believed that it's possible, but makers have not released any software to do it). The only card that actively supports firmware upgrades is the EZ Flash Vi.
To sum it up, the firmware is like the bios of a computer and the kernel is the operating system. To upgrade a firmware (bios), you have to flash it. To upgrade a kernel (operating system) it's a simple exchanging of files.