I'm curious, we have a very well rounded astrological system in Tamriel, but who was it that coined the commonly used astrological phrases and terminologies we use today?

Is it ever established which astronomers and astrologers are responsible for marking the heavens, or is it simply left to assumed that this is passed down tradition, and the discoverers remain nameless?

I'm pretty sure that what the emporer's mananauts used were the records of Dwemer astronomers; we have complete observatories. Of course, the Firmament is a modernized collection of what has been known for ages, and the creation myths all speak of the formations, so the lore has been pretty well established prior to Dwemer's star charting.

In other words; its based on ancient, and well established lore, certainly dating past the Dwemer.