An FM translator is required to have an "originating station". The originating station can be an AM, or FM, or an HD2, HD3, or HD4. Are you saying that the FM translators are originating their own programming, without originating on an AM, FM, or HD channel? HD1 is simply the digital version of the analog main channel.
FM translators aren't specifically classified as "HD" translators. IF the FM station doesn't have HD2 for example, and if the FM translator isn't "translating, ie repeating" but is originating programming, then this is a violation of FCC Regs, and subject to FCC action.
FCC Regs require Call Sign identification. I believe that in the case of an FM translator rebroadcasting HD2 programming, there should be 2 call signs - one airing on the HD channel, "KXXX HD2 Pasco", plus one for the FM translator, "K246CU". Some FM translators have sub-audible call sign capability, which is legal for translators. Also FM translators don't need call sign ID every hour, there are different requirements.