There is, as far as I am aware, no expression which describes the act of putting forward a watch several minutes in order to prevent tardiness or chronic lateness. With the advent of cell/mobile/smart phones, laptops etc., wristwatches will becoming obsolete (in my opinion) and any need for coining such a phrase or word is doomed.
Instead the OP could use several timely expressions to describe his aunt's strategy. The first that sprang to mind was precautious. But that's a bit tedious and uninspiring, so bearing in mind that time is of essence, may I suggest the following expressions and idiom (with tongue stuck firmly in cheek).
- Anticipator, n.
- Ahead of time, idiom.
My aunt is always ahead of time
- Anachronistic, adj.
when something (or someone) is chronologically misplaced
- Chronologist, n.
- Horologist, n.
an expert in horology
- Timesaver, adj., n.
- Watchful, adj.
- Watchwoman, n. (from the established noun watchman)