There are (at least) two possible sources of indeterminacy: (i) a discrepancy between the granularities of the temporal qualification and the occurrence time; (ii) an underspecification of the occurrence time, when the granularities of the temporal qualification and the occurrence time coincide.
The proposed definition of temporally-indeterminate event is: ``a temporally-indeterminate event is an event that is known to have occurred but precisely when is unknown''. Reformulated in terms of statements it becomes: ``a temporally-indeterminate statement is a statement that allows us to conclude that an event has occurred, but it does not tell us precisely when it has occurred.''
Chronologically-indefinite statements are also temporally indeterminate, but not vice versa: temporally-indeterminate statements can be chronologically indefinite as well as chronologically definite.
The statements ``Jack was killed on xx/xx/1990'' and ``Michelle was born yesterday'' come within different categories with respect to the chronological definiteness/indefiniteness characterization, but they are both temporally indeterminate.
As a first approximation, we can say that a statement is temporally indeterminate if the granularity of its temporal qualification (in the examples, the granularity of days) is coarser than the granularity of the time at which the denoted events (instantaneously) occur. Notice that temporal indeterminacy as well as chronological indefiniteness are mainly qualifications of statements rather than of the events they denote (better, temporal indeterminacy characterizes the relation between the granularities of the statement temporal qualification and of the event occurrence time). Notice also that it does not depend on the time at which the statement is evaluated. The crucial, and critical, point is clearly the determination of the time granularity of the event occurrence time.
Some problems could be avoided by adopting the following weaker notion of temporally indeterminacy: a statement whose temporal qualification has granularity G (to say, days) is temporally determinate with respect to every coarser granularity (e.g., months) and temporally indeterminate with respect to every finer granularity (e.g., seconds).
However, we do not like this solution, because it does not take into account information about the denoted events. In particular, for each event there exists a limit time granularity such that its occurrence time can be specified at such a granularity and all coarser ones, but not at finer ones. With respect to each finer granularity, the event as a whole does not make sense at all and it must decomposed into a set of components (if possible).
Let us go back to the proposed definition of temporal indeterminacy to discuss the following issue: does temporal indeterminacy always involve a discrepancy between temporal qualification (expressed as a valid time) and occurrence time granularities? Consider the sentence: ``The shop remained open on a Sunday in April 1990 all the day long''. Clearly, the truth value of the statement does not depend on its utterance time, that is, the statement is chronologically defined. Furthermore, day is the granularity of both the temporal qualification and the occurrence time. Nevertheless, we believe that this statement is temporally indeterminate, because the precise day in which the shop remained open is unknown (we only know that it belong to the set of Sunday days in April 1990).
These sources of indeterminacy are not exclusive and they can jointly contribute to make a statement temporally indeterminate. This is the case, for instance, in the sentence: ``Jack was killed on a Friday night in 1990''.