McMahan's view is meant to justify rejecting the cure, so the agent deciding whether or not to take the cure presumably shouldn't feel compelled to take into account the contingent time-relative interests they would have in future only if they take the cure. Instead, proponents of the Time-Relative Interests Account (TRIA) should most plausibly accept the necessitarian view that we should only count interests that will exist whichever choice the agent makes. In the case of The Cure, that effectively means only considering the time-relative interests the agent has up to the time of choice, which favour rejecting the cure.
So far, so good. But I want to consider an objection to this necessitarian view that Ben Bradley raises in 'The Worst Time to Die' (pp. 312-3):
Suppose Mikey has no interest in trying a certain sort of food, but Jane says to him, “Try some. You’ll like it.” Mikey tries it, and he likes it. As a result of his decision to try the food, he desires that he be eating that food, and since he’s eating it, his eating it is intrinsically good for him. According to necessitarianism, his decision to try the food was not good for him at all. Had he chosen not to try it, he would not have had the desire to be eating it, so his eating it would not have been intrinsically good for him.
This strikes me as simply mistaken, due to conflating desires with interests. Even on a desire-based account of wellbeing, it doesn't follow that whether P best serves your interests is determined simply by whether you desire that P. We have many desires, after all, and our acts can have many consequences, so we must look at how one's total desire-set is affected by total consequences of so acting. Even if you lack an antecedent desire for caviar as such, you likely have an antecedent desire for pleasure, so if trying caviar would (it turns out) give you pleasure, then the necessitarian has no trouble at all explaining why that's in your interests.
Further, we should reject desire theories of wellbeing. Pleasure is pro tanto good whether you desire it or not. So Mikey's welfare interest in pleasurable gustatory experiences isn't in any way contingent on his decision to try the new food. So there's simply no objection to necessitarianism here.
P.S. It's worth flagging that necessitarianism functions in an interestingly different way within TRIA (given an objective conception of wellbeing) than within desire theories of wellbeing. For desire theories, necessitarianism answers the question of what the basic goods are (answer: just those things which satisfy desires the agent has or will have independently of the choice in question). This might help us to rule out induced desire satisfactions as lacking genuine value, for example. But welfare objectivists (objective list theorists) don't take the basic goods to vary or be contingent in the way that desire theories imply. So necessitarianism can't play that role for objectivist proponents of TRIA. Its role is instead, in effect, to determine which possible time-slices of an agent should have their time-relative interests counted. That is, rather than determining whether some possible future is a good one, it determines (e.g.) whether a presumptively good future is one that this agent has a prudential interest in. It's an interesting difference, and one that I think helps to insulate necessitarian objectivist TRIA from some of the objections that might apply to necessitarian desire theories. (Mikey obviously has an interest in his post-trying-new-tastes future, after all, which helps to reveal why Bradley's objection is a non-starter.)