Well, to me the plant looks very healthy. Obviously I can't comment on how fast it's growing without being there to see its progress, but from the photo you took, I wouldn't be too concerned. Just be patient. These grow fastest in warm spring and summer months, then slow down when temperatures and light drop in the fall and winter. The growths can take approximately anywhere from 6 - 9 months to grow to mature size, depending on a lot of factors, so you'll have to take a wait and see approach until you've had the plant long enough to know what's normal under your care.
Several things might be contributing factors here:
1. You recently purchased the plant, so it is still acclimating to your care.
2. The plant looks recently repotted (the bark on top is very fresh looking), and if it was repotted before it was ready, that may cause it to stall a bit.
3. If the plant is not getting strong enough light or the temperatures are too cool, it might have gone into "semi dormancy", where it has reduced its growing metabolism. Maybe you can use the supplemental light every day, unless you're certain the window light alone is bright enough.
M. spectabilis likes lots of bright light, lots of water, and lots of air movement (bright, airy, humid, and warm is ideal). In the warm summer months, and in an airy mix, it's tough to over water them, they can practically sit in water. This time of year, you have to be careful with the watering, but those tiny, wiry roots are an indication that the plant shouldn't be allowed to get too dry.
Do some reading about Miltonia spectabilis online. Since it's a species, and one of the more spectacular (i.e. spectabilis) of the genera, there will be lots of information for you. Just be extremely skeptical about your information resources on this plant. Lots of confusion out there, lots of misinformed people, and lots of incorrect advice because people willfully or otherwise treat Miltonia and Miltoniopsis as being the same thing -- they aren't, and their care can be quite different, especially when it comes to temperatures.
Last edited by MrHappyRotter; 02-16-2017 at 11:08 AM..