I suspect there's confusion over what it means to have different discount rates / utility functions at different times. This could mean either that utility depends on the time (call it τ) at which it's computed, or on the time (call it t) at which utility-bearing events occur. The latter alone is always OK, whether or not the relationship is exponential. The former alone might create dynamic inconsistency, and if so, probably (always?) a money pump. Dependence on t-τ (i.e., 'discounting' as usually conceived of) is dynamically consistent if and only if the relationship is exponential.