You are actually a little bit incorrect.

In the vein of words like homophobia, these words' definitions are not strictly in line with their etymology. Per every dictionary (but quoting Webster), transphobia is defined as:

irrational fear of, aversion to, or discrimination against transgender people

And this might create some linguistic ambiguity, but I cannot seem to find actual documentation on a medical or psychological fear of transgender people at all. It seems this behavior is entirely (or almost entirely) a learned bigotry.

The other word, "transmisia", has not really been officially adopted in any circle I can find. The only place I could find it with any prominance is a site called the "Trans Language Primer", and I know nothing about it (except that it looks like geocities) so I won't be linking it directly. Suffice to say, they speak negatively of the term (despite defending it as having a good intention) and favor "transphobia" for reasons of clarity.