It seems unclear when exactly the Drifter gains the ability to control a warframe.
New Wars shows that he learned that after Lotus was revived.
Duviri Paradox shows that he learned that in Teshin's cave, which is supposed to happen before she reaches Origin system through Zarimen ship.
Here are my 3 theories, but none of them fully explains it.
1. Lotus' hand did Transference in Duviri, Drifter can't. This theory explains why Drifter loses Transference during New War, because he used it to revive the Lotus.
However, it doesn't make sense that Lotus' hand can control the warframe, because if so, the Orokin would never need the Void Children to fight the Old Wars, they just need to produce 1 million Lotus' hand and then everyone in the world could control the warframe.
2. Lotus' hand contain the knowledge, Drifter has the void power.
Since Lotus taught the Tenno about the knowledge of Transference and the hand might contains some memory of it, Drifter combined the knowledge and his power. However, Drifter later told Ordis he has not learn it yet, it doesn't sounds like Drifter somehow forget Transference.
3. Eternalism, New War Drifter and Duviri Drifter are two separate persons.
This theory sounds cheap, and there are several signs that they are the same person. For example, if we customize the New Wars Drifter in the Transference room, the Duviri Drifter also changes their look.