Very definitely NOT cumulative. It says "Whenever you pass a Psychic test for Eldrad Ulthran, you can add 1 to the next Psychic test you take for him until the end of the phase", and not "add one to your Psychic Tests for the rest of the phase". So if Eldrad casts Smite successfully, his next power is 1 easier, and if he casts that, the one afterwards is ALSO 1 easier. Definitely not cumulative.
The only reason it has the "until the end of the phase" rider is because they want to point out that this doesn't last through to your next turn (such that if his last power goes off for the turn, your first power next turn for him does NOT benefit from the +1)..
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