Personal record faster than any of my splits?

If it is your Garmin device (as opposed to the cloud-based Garmin Connect service, after the activity data has been uploaded) that is checking for your best time for various intervals of preset length (1‑km, 1‑mile, 5‑km, etc.), then your marking of laps or splits is simply irrelevant to that functionality and does not affect it.

If you ran a series of (say, fifteen) 400-metre laps only, your Garmin device will still determine your best times for 1‑km, 1‑mile, and 5‑km over the entirety of the timed activity, to test against your previous personal records on the device.

Equally, if your fastest mile over a three-mile run straddles two laps/splits (however long those are), then that is the time that the device will capture – even though it will not capture the start and end points used and tell you somehow. It chooses the one-mile stretch for determining your best mile; you don't.

I actually find it far more useful than if it only stuck with what I designate as a kilometre split, since it is possible for me to review per-lap (or per-split) information from an uploaded activity in Garmin Connect to determine which of my designated splits is fastest, but I cannot possibly do what the watch can do, which is identify my best kilometre and best five-kilometre performance in spite of my manual laps. It doesn't take into account terrain, temperature, wind speed, where anyone normally starts or stops, but simply tells me that I have achieved m:ss over one contiguous kilometre when the conditions are ‘right’ – so that's my personal record. Not my personal record when I run a particular track or segment, just my best kilometre.

If it is your Garmin device (as opposed to the cloud-based Garmin Connect service, after the activity data has been uploaded) that is checking for your best time for various intervals of preset length (1‑km, 1‑mile, 5‑km, etc.), then your marking of laps or splits is simply irrelevant to that functionality and does not affect it.

If you ran a series of (say, fifteen) 400-metre laps only, your Garmin device will still determine your best times for 1‑km, 1‑mile, and 5‑km over the entirety of the timed activity, to test against your previous personal records on the device.

Equally, if your fastest mile over a three-mile run straddles two laps/splits (however long those are), then that is the time that the device will capture – even though it will not capture the start and end points used and tell you somehow. It chooses the one-mile stretch for determining your best mile; you don't.

So I really did run an 8:03 mile? wow

Thanks for the explanation! :)