How can I segment users based on the exact time (including minutes) they last opened the app?

In the Control Panel's segment builder, the default Last Application Open tag and the PW_ApplicationOpen event can only be filtered with day-level windows ("during the last N days", "on a specific date", and so on). So you cannot build a "last 15 minutes" segment from the UI.

You do not need a custom tag or any app-side development, though. The segmentation language supports minute-level precision on any Date tag through the minutesago operator, so you can create the segment with the Segmentation Filters API (/createFilter):

T("Last Application Open", minutesago, lte, 15)

Available operators:

• minutesago lte N — within the last N minutes. Example: T("Last Application Open", minutesago, lte, 30).
• minutesago gte N — N or more minutes ago. Example: T("Last Application Open", minutesago, gte, 60).

The same operator works on any custom Date tag, if you prefer to record your own timestamp:

1. Create a custom Tag: go to Audience > Tags, click Add tag and create a tag of type Date, for example LastOpenTimestamp.
2. Update it from your app: use the SDK's setTags method to write the current timestamp every time the user opens the application.
3. Filter it: T("LastOpenTimestamp", minutesago, lte, 15).

See the segmentation language reference for the full list of Date tag operators.