My headcanon is that Ultra Magnus' role was similar to Alpha Trion's from Five Faces of Darkness. In FFoD we see Sentinel Prime get gunned down by Megatron, and he hands the Matrix to Alpha Trion, who is described as having held it until a new worthy Prime could be found, which ended up being Orion/Optimus. Back then Alpha Trion wasn't a Prime, so I just assumed that sometimes the person a dying Prime passes the Matrix to is deemed worthy and becomes a Prime themself, and sometimes they're not, and they just watch over the Matrix until someone worthy comes along. Ultra Magnus and Alpha Trion were in the latter category.
There's no evidence or indication that Alpha Trion actually carried the Matrix inside his chest as a proper Matrix bearer, though.
But of course, that possibility is something that fans have debated about over the years, and is a big reason why I suspect that the Alpha Prime mentioned in Dreamwave's MTMTE #8 profile book may well have been the Dreamwave G1 version of Alpha Trion as a proper Matrix-bearing Prime before he became "Trion", as Dreamwave had a tendency to canonize or simply lean into things that fans either believed or speculated about that originally had no such confirmation, back in the pre-2000s.
For example, in Marvel UK, Ultra Magnus was not an official member of the Wreckers, just a close associate of them who often worked alongside them. But some fans felt that he might as well have been a Wrecker because of that close association he had with them. Come the early 2000s and Dreamwave introduces their version of the Wreckers with Ultra Magnus not only as a full-fledged member but as their actual leader (in the present-day comics, that is. War Within made Springer their past leader).
As a more relevant example, Dreamwave canonized the idea of Orion Pax becoming Optimus Prime upon obtaining the Matrix (in the exact same vein as how the Matrix turned Hot Rod into Rodimus Prime in TFTM), which only further fueled the debates about whether or not Alpha Trion in the G1 cartoon actually used the Matrix to remake Orion Pax into Optimus Prime in "War Dawn".