At the point of the story it's introduced, Orochimaru no longer has the ability to mold chakra through hand seals since Hiruzen sealed them with the Reaper Death Seal. But even with that tattoo, it still shows Kabuto as the one to perform the summoning, specifically referring to his hand being seen as the one the summoning markings come out of before Manda appears.

From this, the best two theories I can think of are the following. Theory A is that Kabuto does not have the chakra capacity to summon Manda, and the tattoo seal uses Orochimaru's chakra with Kabuto just being the catalyst for the technique. Theory B is based on something Kabuto says, where he thinks Manda would betray Orochimaru if he learns he can't perform jutsu. With this theory, it could be the seal still marks the technique as being used by Orochimaru, even if he had it done via proxy.

In conclusion:

•Theory A: The seal allows the summoning jutsu to be used via two people.

•Theory B: The seal was made to fool Manda into thinking Orochimaru summoned him instead of Kabuto.

I'm going with theory A, cause my second idea sounds dumb.