Yeah, they ran into real problems when later titles came out.
The original C&C was released as "Command & Conquer Teil 1: Der Tiberiumkonflikt" ("tiberium conflict", instead of "tiberian dawn")
The original RA was released as "Command & Conquer Teil 2: Alarmstufe Rot" ("code red", instead of "red alert")
C&C2 was then released as "Command & Conquer Teil 3: Operation Tiberian Sun" (instead of simply "tiberian sun")
By the time C&C2 had been released the Internet was becoming a thing and still predominantly English so the different numbering schemes began causing trouble for English-speaking Germans.
I think they gave up on consistent numbering by the time RA2 came out (it wasn't actually called "Teil 4" IIRC) and if I recall correctly they just stuck to the English numbers with C&C3 onwards (yes, that means technically "C&C3" was ambiguous in Germany at that point).
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In Red Alert there are some clues that the setting is tied to that of the original Command & Conquer however. For example Kane shows up on the Soviet side and it's strongly hinted that he is the same Kane as in Tiberian Dawn. This led to some fan theories that Kane is immortal because he's literally the Biblical character Cain, which was pretty plausible if you consider the other Biblical references ("the land of Nod" is where Cain was exiled and Kane is the leader of the Nod Brotherhood; Seth is Kane's second in command and also the name of Cain's and Abel's brother). I think there were also some conspiracies based on the re-use of German voice actors (I think Einstein's assistant was voiced by the voice actor who also voiced Kane? I don't think this is the case in the English version).
</spoilers>
Ultimately this probably has more to do with budget constraints and that Biblical imagery is a cheap way to introduce some drama and I'm not sure whether this was ever intended as more than a not-so-subtle nod (heh) to Tiberian Dawn.
Fun fact: one major criticism of Tiberian Sun was that the publisher cast a new voice actor for Kane who sounded nothing like the first one fans had grown to love (his voice was also much lighter, leading many to joke that he sounded a bit emasculated). IIRC the official explanation was that the original voice actor had demanded too much money. In addition to the disproportionate hype the game had received prior to release that was also often pointed out as one of the major reasons it wasn't as successful as anticipated.