The origin of this term comes from the grand MOBA of all of them: the WC3 map "DOTA".
In Warcraft 3 generally the characters learned on level 6 their so called "ultimate" (I'm actually not even sure they had a name or in general just were named ultimate).
So of course these special match making abilities were in the DOTA map called "ultimates" as well. This obviously abbreviated into "ult" or "ulti".
In this regard the term was pulled into all games that were direct siblings of that WC3 map, if not by the devs, then by the community as they had been used to calling it that way.
But this is just true for siblings of DOTA (i.e. not for all MOBAs). For example, in Awesomenauts there is no equivalent of overskill like the ultimates from WC3. Therefore, no one would name them as "ultimates".